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1
Santos, Djair Paulino dos. "Hiper-ideais de operadores entre espaços de Banach." Universidade Federal da Paraíba, 2017. http://tede.biblioteca.ufpb.br:8080/handle/tede/9282.
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Previous issue date: 2017-03-06<br>Conselho Nacional de Pesquisa e Desenvolvimento Científico e Tecnológico - CNPq<br>In the present work we investigate topics of the theory of multi-ideals and hyperideals,
introduced by Botelho and Torres. We also investigate the connection between
the concept of hyper-ideals and the notion of coherence of multi-ideals.<br>No presente trabalho estudaremos t opicos da teoria de multi-ideais e da recente
teoria de hiper-ideais, introduzida por Botelho e Torres. Estudaremos ainda a rela c~ao
entre o conceito de hiper-ideais e a no c~ao de coer^encia de multi-ideais.
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Mascia, Carla. "Ideals generated by 2-minors: binomial edge ideals and polyomino ideals." Doctoral thesis, Università degli studi di Trento, 2020. http://hdl.handle.net/11572/252052.
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Since the early 1990s, a classical object in commutative algebra has been the study of binomial ideals. A widely-investigated class of binomial ideals is the one containing those generated by a subset of 2-minors of an (m x n)-matrix of indeterminates. This thesis is devoted to illustrate some algebraic and homological properties of two classes of ideals of 2-minors: binomial edge ideals and polyomino ideals.
Binomial edge ideals arise from finite graphs and their appeal results from the fact that their homological properties reflect nicely the combinatorics of the underlying graph. First, we focus on the binomial edge ideals of block graphs. We give a lower bound for their Castelnuovo-Mumford regularity by computing the two distinguished extremal Betti numbers of a new family of block graphs, called flower graphs. Moreover, we present a linear time algorithm to compute Castelnuovo-Mumford regularity and Krull dimension of binomial edge ideals of block graphs. Secondly, we consider some classes of Cohen-Macaulay binomial edge ideals. We provide the regularity and the Cohen-Macaulay type of binomial edge ideals of Cohen-Macaulay cones, and we show the extremal Betti numbers of Cohen-Macaulay bipartite and fan graphs. In addition, we compute the Hilbert-Poincaré series of the binomial edge ideals of some Cohen-Macaulay bipartite graphs.
Polyomino ideals arise from polyominoes, plane figures formed by joining one or more equal squares edge to edge. It is known that the polyomino ideal of simple polyominoes is prime. We consider multiply connected polyominoes, namely polyominoes with holes, and observe that the non-existence of a certain sequence of inner intervals of the polyomino, called zig-zag walk, gives a necessary condition for the primality of the polyomino ideal. Moreover, by computational approach, we prove that for all polyominoes with rank less than or equal to 14 the above condition is also sufficient. Lastly, we present an infinite class of prime polyomino ideals.
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Mascia, Carla. "Ideals generated by 2-minors: binomial edge ideals and polyomino ideals." Doctoral thesis, Università degli studi di Trento, 2020. http://hdl.handle.net/11572/252052.
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Since the early 1990s, a classical object in commutative algebra has been the study of binomial ideals. A widely-investigated class of binomial ideals is the one containing those generated by a subset of 2-minors of an (m x n)-matrix of indeterminates. This thesis is devoted to illustrate some algebraic and homological properties of two classes of ideals of 2-minors: binomial edge ideals and polyomino ideals.
Binomial edge ideals arise from finite graphs and their appeal results from the fact that their homological properties reflect nicely the combinatorics of the underlying graph. First, we focus on the binomial edge ideals of block graphs. We give a lower bound for their Castelnuovo-Mumford regularity by computing the two distinguished extremal Betti numbers of a new family of block graphs, called flower graphs. Moreover, we present a linear time algorithm to compute Castelnuovo-Mumford regularity and Krull dimension of binomial edge ideals of block graphs. Secondly, we consider some classes of Cohen-Macaulay binomial edge ideals. We provide the regularity and the Cohen-Macaulay type of binomial edge ideals of Cohen-Macaulay cones, and we show the extremal Betti numbers of Cohen-Macaulay bipartite and fan graphs. In addition, we compute the Hilbert-Poincaré series of the binomial edge ideals of some Cohen-Macaulay bipartite graphs.
Polyomino ideals arise from polyominoes, plane figures formed by joining one or more equal squares edge to edge. It is known that the polyomino ideal of simple polyominoes is prime. We consider multiply connected polyominoes, namely polyominoes with holes, and observe that the non-existence of a certain sequence of inner intervals of the polyomino, called zig-zag walk, gives a necessary condition for the primality of the polyomino ideal. Moreover, by computational approach, we prove that for all polyominoes with rank less than or equal to 14 the above condition is also sufficient. Lastly, we present an infinite class of prime polyomino ideals.
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Lima, Pedro Henrique Apoliano Albuquerque. "Multiplicidade de ideais e números de Segre." Universidade de São Paulo, 2008. http://www.teses.usp.br/teses/disponiveis/55/55135/tde-02092009-100114/.
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Neste trabalho, estudamos a multiplicidade de Hilbert-Samuel, e suas possíveis generalizações, tais como números de Segre e a sequência de multiplicidades de Achilles e Manaresi<br>In this work is studied the multiplicity of Hilbert-Samuel and its possible generalizations, such as Segre numbers and sequence of multiplicities of Achilles and Manaresi
5
Liu, Yu-Han. "Gradient ideals." The Ohio State University, 2010. http://rave.ohiolink.edu/etdc/view?acc_num=osu1280803107.
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SECCIA, LISA. "Knutson ideals." Doctoral thesis, Università degli studi di Genova, 2021. http://hdl.handle.net/11567/1049960.
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In this thesis, we begin the study of a new class of ideals, called Knutson ideals, which has several useful connections with different aspects of commutative algebra, such as $F$-singularity theory, Gr"obner basis theory, determinantal rings theory and combinatorics.
First, we show that the main properties that this class has in polynomial rings over F_p are preserved when one introduces the definition of Knutson ideal also in polynomial rings over fields of characteristic zero.
Then, we discuss the case of determinantal ideals of Hankel matrices and generic matrices, proving that both of them are Knutson ideals. In particular, in positive characteristic, they all define F-pure rings.
In the case of Hankel matrices, we also give a characterization of all the ideals belonging to the family. Interestingly, it turns out that they are all Cohen-Macaulay ideals.
In the case of generic matrices, we obtain a useful result about Gr"obner bases of certain sums of determinantal ideals. More specifically, given I = I_1 +...+ I_k a sum of ideals of minors on adjacent columns or rows, we prove that the union of the Gr"obner bases of the I_j's is a Gr"obner basis of I.
Lastly, we focus on the connection between Knutson ideals and binomial edge ideals associated to weakly closed graphs. Inspired by Matsuda's work on weakly closed graphs, we show that their binomial edge ideals are Knutson ideals (in particular, they are F-pure in positive characteristic). Furthermore, we conjecture that the converse is still true, i.e, the binomial edge ideals in C_f are exactly those associated to weakly closed graphs.
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Ennis, William Thomas. "Hereditarian ideas and eugenic ideals at the National Deaf-Mute College." Diss., University of Iowa, 2015. https://ir.uiowa.edu/etd/1966.
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For the past two centuries deaf people in the United States have faced more or less intense skepticism about their marriages to each other, largely due to fears of inherited deafness. Theses fears, while always present, have waxed and waned over time, becoming most prominent during the eugenics era of the late nineteenth and early twentieth centuries. At Gallaudet University, they were repeatedly expressed by the faculty and administration in a variety of forms and contexts, and echoed by many its students. This dissertation demonstrates the significant influence of these ideas at Gallaudet University on the wider deaf community over the last century; it traces how skepticism toward deaf marriage was framed in terms of hereditarian and, for a time, eugenic ideals; and it explored other more subtle but similarly effective attempts to influence marriage decisions by deaf people. The idea that deaf people should not marry one another was embraced by faculty in Gallaudet’s early decades, diffused from administration to faculty, from faculty to students (deaf undergraduates as well as hearing students studying deaf education), and ultimately carried to other deaf educational institutions via the alumni. While student responses to these ideas were fluid, their adoption by early administration and faculty had a profound and lasting impact. One result was that, during much of the early twentieth century, deaf people were less likely to marry, and when married less likely to have children.
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Bowman, Pamela. "Ideals and Realities." Diss., CLICK HERE for online access, 2005. http://contentdm.lib.byu.edu/ETD/image/etd1082.pdf.
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LOPES, DUARTE LUIS PEDRO. "Perturbations of ideals." Doctoral thesis, Università degli studi di Genova, 2023. https://hdl.handle.net/11567/1105884.
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Let I be an ideal of a Noetherian local ring R. We study how properties of the ideal change under small perturbations, that is, when I is replaced by an ideal J which is the same as I modulo a large power of the maximal ideal. In particular, assuming that R/J has the same Hilbert function as R/I, we show that the Betti numbers of R/J coincide with those of R/I. We also compare the local cohomology modules of R/J with those of R/I.
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Medeiros, Luan Benzi. "Ideais diferenciais em álgebras finitamente geradas." Universidade de São Paulo, 2018. http://www.teses.usp.br/teses/disponiveis/55/55135/tde-24102018-101842/.
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O objetivo principal dessa dissertação é o estudo do comportamento de ideais diferenciais com respeito à importantes temas de álgebra comutativa como decomposição primária e localização. Veremos que dado um ideal diferencial em um anel noetheriano de característica zero, seus primos associados também serão diferenciais e que ele admite uma decomposição primária cujas componentes são diferenciais. Em relação a localização, teremos uma equivalência dos conceitos de ideais diferenciais no anel dado e no localizado, ou seja, um ideal é diferencial se, e somente se, sua localização também o é.<br>The main goal of this dissertation is to study the behavior of differential ideals regarding important themes of commutative algebra such as primary decomposition and localization. We will see that, given a differential ideal in a noetherian ring of caracteristic zero, its associated primes ideals will also be differentials and we will exhibit a primary decomposition whose components will be differentials too. In relation to localization, we will have an equivalence of the concepts of differential ideals in the given ring and in the localized ring, that is, an ideal is differential if, and only if, its localization is differential too.
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Henriksson, Amadeus. "Ideal i dagens planeringspraktik : Teorier och ideals inverkan på den svenska översiktsplaneringen." Thesis, Blekinge Tekniska Högskola, Institutionen för fysisk planering, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:bth-14409.
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En strategisk fysisk planering har under flera år varit något som förespråkats från statligt håll i Sverige, men trots detta så har idealen inte fått något tydligt fäste i den kommunala planeringen. Det är utifrån detta glapp mellan teori och praktik som arbetet har sin utgångspunkt, där syftet är att skapa en förståelse för planeringsprocessens underliggande ideal, sättet som idealen påverkar planeringen och anledningen till att glappet mellan teori och praktik har uppkommit. Dagens planeringspraktik studeras utifrån sex översiktsplaneprocesser, där ideal från den rationella, kommunikativa och strategiska planeringen identifieras och lyfts fram. Utifrån intervjuer gjorda med kommunala planerare så dras slutsatsen att dagens översiktsplanering främst är baserad på ett rationellt ideal, vilket synliggörs av den systematik och regelstyrning som finns i processen och genom den tydliga rollfördelning som finns mellan planerare och politiker. Uppsatsen visar också på att den kommunikativa teorin inte har fått det genomslag som planeringsdebatten möjligen ger sken av, utan har främst inneburit att ett större antal aktörer inkluderas i processen och att det skapats en bredare kunskapssyn. Den strategiska fysiska planeringen har främst inkluderats genom användandet av visioner, men där dessa är begränsade till att ge en riktning åt den kommunala planeringen och utgår inte från teorins konsensusbyggande eller aktörsmobiliserande aspekter. Arbetet visar på att idealet om en strategisk fysisk planering, som förespråkas från statligt håll, inte har fått något genomslag eftersom praktiker eftersträvar ett rationellt ideal snarare än ett strategiskt. Ett första steg för att glappet mellan teori och praktik ska minska skulle i så fall vara att praktiker och statliga myndigheter eftersträvar samma ideal. Det går att härleda det rationella idealet bland planerare till att planeringssystemet i sig är rationellt uppbyggt och att planerare endast i liten utsträckning går utöver de lagstadgade kraven i sitt arbete. Glappet mellan teori och praktik har därför förstärkts av att planeringssystemet inte har förändrats i tillräckligt utsträckning, men har också påverkats av att planerare inte aktivt reflekterar över sättet som de arbetar på. Samtidigt bemöts de kommunikativa och strategiska idealen som fått genomslag av ett starkt motstånd från det rationella planeringssystemet, vilka gör att de endast delvis kunnat bli implementerade.
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Moura, Fernanda Ribeiro de. "Ideais algebricos de aplicações multilineares e polinômios homogêneos." Universidade Federal de Uberlândia, 2014. https://repositorio.ufu.br/handle/123456789/16812.
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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior<br>The main purpose of this dissertation is the study of ideals of multilinear mappings and
homogeneous polynomials between linear spaces. By an ideal we mean a class that is
stable under the composition with linear operators. First we study multilinear mappings
and spaces of multilinear mappings. We also show how to obtain, from a given multilinear
mapping, other multilinear mappings with degrees of multilinearity greater than, equal
to or smaller than the degree of the original multilinear mapping. Next we study homogeneous
polynomials and spaces of homogeneous polynomials, and we also show how
to obtain, from a given n-homogeneous polynomial, other polynomials with degrees of
homogeneity greater than, equal to or smaller than the degree of the original polynomial.
Next we study ideals of multilinear mappings, or multi-ideals, and ideals of homogeneous
polynomial, or polynomial ideals, giving several examples and presenting methods to generated
multi-ideals and polynomial ideals from a given operator ideal. Finally we dene
and give several examples of coherent multi-ideals and coherent polynomial ideals.<br>O principal objetivo desta dissertação e estudar os ideais de aplicações multilineares e polinômios homogêneos entre espaços vetoriais. Por um ideal entendemos uma classe de aplicações que e estavel atraves da composição com operadores lineares. Primeiramente estudamos as aplicações multilineares e os espaços de aplicações multilineares. Mostramos tambem como obter, a partir de uma aplicação multilinear dada, outras aplicações com graus de multilinearidade maiores, iguais ou menores que o da aplicação original. Em seguida estudamos os polinômios homogêneos e os espacos de polinômios homogêneos,
e mostramos que, a partir de um polinômio n-homogêneo, tambem podemos construir novos polinômios homogêneos com graus de homogeneidade maiores, iguais ou menores que n. Posteriormente estudamos os ideais de aplicações multilineares, ou multi-ideais,
e os ideais de polinômios homogêneos, exibindo varios exemplos e apresentando metodos para se obter um multi-ideais, ou ideais de polinômios, a partir de ideais de operadores lineares dados. Por m, denimos e exibimos varios exemplos de multi-ideais coerentes e
de ideais coerentes de polinômios.<br>Mestre em Matemática
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Vold, Eirik Holteberg. "Unique Factorization of Ideals." Thesis, Norges teknisk-naturvitenskapelige universitet, Institutt for matematiske fag, 2013. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-23680.
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Egan, Matthew. "Generalizations of prime ideals." Thesis, McGill University, 1989. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=61892.
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Nigussie, Yared. "Tree ideals and algorithms /." The Ohio State University, 1999. http://rave.ohiolink.edu/etdc/view?acc_num=osu1488187049542378.
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Boswell, Schiefer Ellen W. "Miracle at Monte Oliveto Renaissance Benedictine Ideals and Humanist Pictorial Ideals in Perspective." University of Cincinnati / OhioLINK, 2012. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1337363195.
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Patnaik, Sasmita. "Ideals and Commutators of Operators." University of Cincinnati / OhioLINK, 2012. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1353343026.
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edu, wodzicki@math berkeley. "Commutator Structure of Operator Ideals." ESI preprints, 2001. ftp://ftp.esi.ac.at/pub/Preprints/esi1062.ps.
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Altafi, Nasrin. "Lefschetz Properties of Monomial Ideals." Licentiate thesis, KTH, Matematik (Inst.), 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-223373.
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This thesis concerns the study of the Lefschetz properties of artinian monomial algebras. An artinian algebra is said to satisfy the strong Lefschetz property if multiplication by all powers of a general linear form has maximal rank in every degree. If it holds for the first power it is said to have the weak Lefschetz property (WLP). In the first paper, we study the Lefschetz properties of monomial algebras by studying their minimal free resolutions. In particular, we give an afirmative answer to an specific case of a conjecture by Eisenbud, Huneke and Ulrich for algebras having almost linear resolutions. Since many algebras are expected to have the Lefschetz properties, studying algebras failing the Lefschetz properties is of a great interest. In the second paper, we provide sharp lower bounds for the number of generators of monomial ideals failing the WLP extending a result by Mezzetti and Miró-Roig which provides upper bounds for such ideals. In the second paper, we also study the WLP of ideals generated by forms of a certain degree invariant under an action of a cyclic group. We give a complete classication of such ideals satisfying the WLP in terms of the representation of the group generalizing a result by Mezzetti and Miró-Roig.<br><p>QC 20180220</p>
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Farah, Ilijas. "Analytic ideals and their quotients." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1997. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp03/NQ27642.pdf.
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Russell, Ewan. "Prime ideals in quantum algebras." Thesis, University of Edinburgh, 2009. http://hdl.handle.net/1842/3450.
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The central objects of study in this thesis are quantized coordinate algebras. These algebras originated in the 1980s in the work of Drinfeld and Jumbo and are noncommutative analogues of coordinate rings of algebraic varieties. The organic nature by which these algebras arose is of great interest to algebraists. In particular, investigating ring theoretic properties of these noncommutative algebras in comparison to the properties already known about their classical (commutative) counterparts proves to be a fruitful process. The prime spectrum of an algebra has always been seen as an important key to understanding its fundamental structure. The search for prime spectra is a central focus of this thesis. Our focus is mainly on Quantum Grassmannian subalgebras of quantized coordinate rings of Matrices of size m x n (denoted Oq(Mm;n)). Quantum Grassmannians of size m x n are denoted Gq(m; n) and are the subalgebras generated by the maximal quantum minors of Oq(Mm;n). In Chapter 2 we look at the simplest interesting case, namely the 2 x 4 Quantum Grassmannian (Gq(2; 4)), and we identify the H-primes and automorphism group of this algebra. Chapter 3 begins with a very important result concerning the dehomogenisation isomorphism linking Gq(m; n) and Oq(Mm;n¡m). This result is applied to help to identify H-prime spectra of Quantum Grassmannians. Chapter 4 focuses on identifying the number of H-prime ideals in the 2xn Quan- tum Grassmannian. We show the link between Cauchon fillings of subpartitions and H-prime ideals. In Chapter 5, we look at methods of ordering the generating elements of Quantum Grassmannians and prove the result that Quantum Grassmannians are Quantum Graded Algebras with a Straightening Law is maintained on using one of these alternative orderings. Chapter 6 looks at the Poisson structure on the commutative coordinate ring, G(2; 4) encoded by the noncommutative quantized algebra Gq(2; 4). We describe the symplectic ideals of G(2; 4) based on this structure. Finally in Chapter 7, we present an analysis of the 2 x 2 Reflection Equation Algebra and its primes. This algebra is obtained from the quantized coordinate ring of 2 x 2 matrices, Oq(M2;2).
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Bouchat, Rachelle R. "ALGEBRAIC PROPERTIES OF EDGE IDEALS." UKnowledge, 2008. http://uknowledge.uky.edu/gradschool_diss/618.
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Given a simple graph G, the corresponding edge ideal IG is the ideal generated by the edges of G. In 2007, Ha and Van Tuyl demonstrated an inductive procedure to construct the minimal free resolution of certain classes of edge ideals. We will provide a simplified proof of this inductive method for the class of trees. Furthermore, we will provide a comprehensive description of the finely graded Betti numbers occurring in the minimal free resolution of the edge ideal of a tree. For specific subclasses of trees, we will generate more precise information including explicit formulas for the projective dimensions of the quotient rings of the edge ideals. In the second half of this thesis, we will consider the class of simple bipartite graphs known as Ferrers graphs. In particular, we will study a class of monomial ideals that arise as initial ideals of the defining ideals of the toric rings associated to Ferrers graphs. The toric rings were studied by Corso and Nagel in 2007, and by studying the initial ideals of the defining ideals of the toric rings we are able to show that in certain cases the toric rings of Ferrers graphs are level.
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Grime, Peter John. "Fitting ideals and module structure." Thesis, Durham University, 2002. http://etheses.dur.ac.uk/3946/.
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Let R be a commutative ring with a 1. Original work by H. Fitting showed how we can associate to each finitely generated E-module a unique sequence of R-ideals, which are known as Fitting Ideals. The aim of this thesis is to undertake an investigation of Fitting Ideals and their relation with module structure and to construct a notion of Fitting Invariant for certain non-commutative rings. We first of all consider the commutative case and see how Fitting Ideals arise by considering determinantal ideals of presentation matrices of the underlying module and we describe some applications. We then study the behaviour of Fitting Ideals for certain module structures and investigate how useful Fitting Ideals are in determining the underlying module. The main part of this work considers the non-commutative case and constructs Fitting Invariants for modules over hereditary orders and shows how, by considering maximal orders and projectives in the hereditary order, we can obtain some very useful invariants which ultimately determine the structure of torsion modules. We then consider what we can do in the non-hereditary case, in particular for twisted group rings. Here we construct invariants by adjusting presentation matrices which generalises the previous work done in the hereditary case.
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Philips, Abraham Ohanaje. "Nonassociative algebras and normal ideals." Thesis, Birkbeck (University of London), 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.251635.
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Jacques, Sean. "Betti numbers of graph ideals." Thesis, University of Sheffield, 2004. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.414677.
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Allen, Stephen David. "Ideals of completely bounded operators." Thesis, University of Edinburgh, 1991. http://hdl.handle.net/1842/11154.
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Sekaran, Rajakrishnar. "Fuzzy ideals in commutative rings." Thesis, Rhodes University, 1995. http://hdl.handle.net/10962/d1005221.
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In this thesis, we are concerned with various aspects of fuzzy ideals of commutative rings. The central theorem is that of primary decomposition of a fuzzy ideal as an intersection of fuzzy primary ideals in a commutative Noetherian ring. We establish the existence and the two uniqueness theorems of primary decomposition of any fuzzy ideal with membership value 1 at the zero element. In proving this central result, we build up the necessary tools such as fuzzy primary ideals and the related concept of fuzzy maximal ideals, fuzzy prime ideals and fuzzy radicals. Another approach explores various characterizations of fuzzy ideals, namely, generation and level cuts of fuzzy ideals, relation between fuzzy ideals, congruences and quotient fuzzy rings. We also tie up several authors' seemingly different definitions of fuzzy prime, primary, semiprimary and fuzzy radicals available in the literature and show some of their equivalences and implications, providing counter-examples where certain implications fail.
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Coughlin, Heather. "Classes of normal monomial ideals /." view abstract or download file of text, 2004. http://wwwlib.umi.com/cr/uoregon/fullcit?p3147816//.
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Thesis (Ph. D.)--University of Oregon, 2004.<br>Typescript. Includes vita and abstract. Includes bibliographical references (leaves 85-86). Also available for download via the World Wide Web; free to University of Oregon users.
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Ahlgren, Joyce Christine. "Ideals, varieties, and Groebner bases." CSUSB ScholarWorks, 2003. https://scholarworks.lib.csusb.edu/etd-project/2282.
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The topics explored in this project present and interesting picture of close connections between algebra and geometry. Given a specific system of polynomial equations we show how to construct a Groebner basis using Buchbergers Algorithm. Gröbner bases have very nice properties, e.g. they do give a unique remainder in the division algorithm. We use these bases to solve systems of polynomial quations in several variables and to determine whether a function lies in the ideal.
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Santos, Diego Cardoso dos. "Potências simbólicas e suas interações." Universidade Federal de Sergipe, 2016. https://ri.ufs.br/handle/riufs/5801.
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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES<br>The notion of symbolic power dates back to W. Krull, who used it in the proof of
the famous theorem of principal ideal, this a crucial milestone in the short history of
commutative algebra. Later, O. Zariski, M. Nagata, D. Rees and others have shown
how this purely algebraic notion has important signi cance in algebraic geometry.
In this paper we study the symbolic powers showing some of its most fundamental
properties and their connections with various aspects of algebraic geometry and
commutative algebra.<br>A no ção de potência simb ólica remonta a W. Krull, que a usou na prova do
c élebre teorema do ideal principal, este um marco crucial na curta hist ória da álgebra
comutativa. Mais adiante, O. Zariski, M. Nagata, D. Rees e outros mostraram como
esta no ção puramente alg ébrica tem importante signi ficado em geometria alg ébrica.
Neste trabalho estudaremos as potências simb ólicas evidenciando algumas de suas
propriedades mais fundamentais e suas conexões com aspectos variados da geometria
alg ébrica e álgebra comutativa.
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Flak, Kimberley. "Selinger's CPM construction and nuclear ideals." Thesis, University of Ottawa (Canada), 2006. http://hdl.handle.net/10393/27357.
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Monoidal categories have recently been seen to be appropriate structures for establishing abstract axioms for quantum physics. The tensor product in a monoidal category corresponds to the creation of a composite system obtained by joining two independent quantum systems. This correspondence is formalized in the work of Abramsky-Coecke and Selinger. From this point of view, the tensor product in a monoidal category is abstracting the tensor product of Hilbert spaces. The notion of a dagger compact closed category axiomatizes further structure in the Hilbert space category. In particular, the dagger is an abstraction of the familiar Hilbert adjoint. Peter Selinger associates to each dagger compact closed category C its category of completely positive maps, denoted CPM(C). He proves that the resulting category is again a dagger compact closed category. We seek a similar result for tensored †-categories equipped with nuclear ideals.
We establish an appropriate notion of completely positive maps in a nuclear ideal. We then define a CPM construction for tensored †-categories equipped with nuclear ideals. Analogous to Selinger's construction, given a nuclear ideal N for a tensored †-category C, our construction yields its category of completely positive maps, CPMN(C). We prove that CPM N(C). is again a tensored †-category. In the process, we also verify that our completely positive maps properly extend Selinger's notion of CPMs. In particular, they preserve nuclear-positive matrices, which are generalizations of von Neumann's positive density operators. As well, we characterize the completely positive maps for the nuclear ideal of Hilbert-Schmidt operators for Hilb and the nuclear ideal of finite relations for LFR. Our construction abstracts the passage from finite-dimensional Hilbert spaces to the category of all Hilbert spaces.
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Reitsma, Regan Lance. "Personal ideals and rationally impotent desires." Columbus, Ohio : Ohio State University, 2007. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1190123916.
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Östlin, Christofer. "Operations on ideals in polynomial rings." Thesis, Uppsala universitet, Algebra och geometri, 2014. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-217839.
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Moore, Dennis. "HILBERT POLYNOMIALS AND STRONGLY STABLE IDEALS." UKnowledge, 2012. http://uknowledge.uky.edu/math_etds/2.
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Strongly stable ideals are important in algebraic geometry, commutative algebra, and combinatorics. Prompted, for example, by combinatorial approaches for studying Hilbert schemes and the existence of maximal total Betti numbers among saturated ideals with a given Hilbert polynomial, three algorithms are presented. Each of these algorithms produces all strongly stable ideals with some prescribed property: the saturated strongly stable ideals with a given Hilbert polynomial, the almost lexsegment ideals with a given Hilbert polynomial, and the saturated strongly stable ideals with a given Hilbert function. Bounds for the complexity of our algorithms are included. Also included are some applications for these algorithms and some estimates for counting strongly stable ideals with a fixed Hilbert polynomial.
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Krone, Robert Carlton. "Symmetric ideals and numerical primary decomposition." Diss., Georgia Institute of Technology, 2015. http://hdl.handle.net/1853/53907.
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The thesis considers two distinct strategies for algebraic computation with polynomials in high dimension.
The first concerns ideals and varieties with symmetry, which often arise in applications from areas such as algebraic statistics and optimization. We explore the commutative algebra properties of such objects, and work towards classifying when symmetric ideals admit finite descriptions including equivariant Gröbner bases and generating sets. Several algorithms are given for computing such descriptions. Specific focus is given to the case of symmetric toric ideals.
A second area of research is on problems in numerical algebraic geometry. Numerical algorithms such as homotopy continuation can efficiently compute the approximate solutions of systems of polynomials, but generally have trouble with multiplicity. We develop techniques to compute local information about the scheme structure of an ideal at approximate zeros. This is used to create a hybrid numeric-symbolic algorithm for computing a primary decomposition of the ideal.
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Akhavizadegan, Mohammad. "Prime ideals of quantized Weyl algebras." Thesis, University of Sheffield, 1997. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.263759.
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Epstein, Melker. "Powers and Products of Monomial Ideals." Thesis, Uppsala universitet, Algebra och geometri, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-298044.
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Ahmed, Shehzad. "Progressive Ideals in Combinatorial Set Theory." Ohio University / OhioLINK, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1554379497651916.
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Chang, Eun R. "Grobner Bases and Ideals of Points." VCU Scholars Compass, 2006. http://scholarscompass.vcu.edu/etd/1214.
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The main point of this thesis is an introduction to the theory of Grobner bases. The concept of Grobner basis and construction of the Grobner basis by Buchberger's Algorithm, in which the notion of S-polynomials is introduced, and a few modified or improved versions of Grobner basis algorithm are reviewed in this paper. In Chapter 1, we have a review of ideals, the definitions and types of monomial ordering, the multivariate polynomial division algorithm and its examples. After ascertaining the monomial ordering on multivariate polynomials, we establish a leading term of a polynomial.In Chapter 2, after defining Grobner bases, we study some nice and useful properties of Grobner bases, such as a uniqueness of reduced Grobner basis and existence of a Grobner basis.In Chapter 3, we explore the Buchberger-Moller algorithm to construct Grobner bases and return a set of polynomials whose residue classes form a basis of a quotient of a polynomial ring. Also, we survey a generalized Buchberger-Moller algorithm to determine directly a Grobner basis for the intersection of a finite number of ideals.In Chapter 4, we conclude this paper with some applications of Grobner bases.
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Grahle, André. "Ideals, reasons, and the second person." Thesis, University of St Andrews, 2014. http://hdl.handle.net/10023/7043.
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The aim of this thesis is to shed light on important aspects of the role ideals play in practical reasoning. In the first chapter an account of ideals as conceptions of admirable ways of being (a true friend, a great athlete, a perfect dandy) is provided, distinguishing proper ideals from bad and incomplete ones. In the second chapter, it is shown what it takes for a person to have an ideal. The phenomenon of ideal possession reveals a complex dispositional structure at the centre of which lies a kind of affective desire, a feeling of a calling to be the way conceptualised by the ideal. Admiration for ideal ways of being observed in real and imaginative others can, under certain conditions, trigger such a desire. In the third chapter, the normative implications of ideal possession are examined. To have an ideal comes with a standing vocational reason to pursue one's ideal. This standing reason, in turn, gives rise to a steady supply of case-dependent vocational reasons to act and to feel in certain ways; reasons that ultimately guide one's attempts at living up to one's ideal. Finally, the fourth chapter investigates the contribution of a pursuit of ideals to the quality of one's life. The main focus is on the kind of recognition that successful idealists are likely to receive from actual admirers. It is argued that second-personal expressions of admiration can endow the idealist with petitionary reasons to maintain or develop her admirable properties. The result is the doubling of reasons: The interplay of both ideal-based vocational reasons and admiration-based petitionary reasons pulling in the same direction, helping the idealist to live a life in which her individual and social natures are better reconciled with each other – a life which is not necessarily happier, but likely more meaningful.
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Levering, Kimery. "Contrast-based ideals constrain graded structure." Diss., Online access via UMI:, 2008.
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Gasanova, Oleksandra. "Properties of powers of monomial ideals." Licentiate thesis, Uppsala universitet, Algebra och geometri, 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-410846.
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Pequignot, Yann. "Better-quasi-order : ideals and spaces." Sorbonne Paris Cité, 2015. http://www.theses.fr/2015USPCC270.
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Cette thèse se situe dans les domaines de la combinatoire, de la théorie des ordres et de la théorie descriptive. La première contribution concerne la théorie des bons quasi-ordres (wqo) et des meilleurs quasi-ordres (bqo). Le résultat principal est la preuve d'une conjecture, énoncée par Pouzet en 1978 dans sa thèse d'état, qui établit que tout wqo dont l'ensemble des idéaux non principaux ordonnés par inclusion forme un bqo est alors lui-même un bqo. La preuve repose sur de nouveaux résultats, qui allient la combinatoire et la topologie, au sujet des fonctions d'un front vers un espace métrique compact. La seconde contribution de cette thèse traite de la complexité topologique dans le cadre des espaces To à base dénombrable. Dans le cas de l'espace de Baire, le quasi-ordre de Wadge est un wqo sur les sous-ensembles Boréliens qui a suscité énormément d'intérêt. Cependant cette relation de réduction par fonctions continues s'avère bien moins satisfaisante pour d'autres espaces d'importance tels que la droite réelle, comme l'ont fait notamment remarquer Hertling, Schlicht et Ikegami. Nous proposons de conserver la continuité et d'affaiblir la notion de fonction pour celle de relation. Pour ce faire, nous utilisons la notion de représentation admissible étudiée en « Type-2 theory of effectivity » initiée par Weihrauch. Nous introduisons alors le quasi-ordre de réduction par relations relativement continues et montrons que celui-ci à la fois raffine les hiérarchies classiques de complexité topologique et forme un wqo sur les sous-ensembles Boréliens de chaque espace quasi-Polonais<br>This thesis deals with combinatorics, order theory and descriptive set theory. The first contribution is to the theory of well-quasi-orders (wqo) and better-quasi-orders (bqo). The main result is the proof of a conjecture made by Maurice Pouzet in 1978 his thèse d'état which states that any wqo whose ideal completion remainder is bqo is actually bqo. Our proof relies on new results with both a combinatorial and a topological flavour concerning maps from a front into a compact metric space. The second contribution is of a more applied nature and deals with topological spaces. We define a quasi-order on the subsets of every second countable To topological space in a way that generalises the Wadge quasi-order on the Baire space, while extending its nice properties to virtually all these topological spaces. The Wadge quasi-order of reducibility by continuous functions is wqo on Borel subsets of the Baire space, this quasi-order is however far less satisfactory for other important topological spaces such as the real line, as Hertling, Ikegami and Schlicht notably observed. Some authors have therefore studied reducibility with respect to some classes of discontinuous functions to remedy this situation. We propose instead to keep continuity but to weaken the notion of function to that of relation. Using the notion of admissible representation studied in Type-2 theory of effectivity, we define the quasi-order of reducibility by relatively continuous relations. We show that this quasi-order both refines the classical hierarchies of complexity and is wqo on the Borel subsets of virtually every second countable To space - including every (quasi-)Polish space
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Elmerstig, Eva. "Painful Ideals : Young Swedish women´s ideal sexual situations and experiences of pain during vaginal intercourse." Doctoral thesis, Linköpings universitet, Genus och medicin, 2009. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-20277.
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Many young women today are concerned about their sexual health; an increasing number of them consult gynaecologists, youth centres (YCs) and general practitioners with vulvar problems such as painful sensations associated with vaginal intercourse (VIC). It is known that some women continue to have VIC despite pain. Theoretically, repeated painful VIC might elicit vaginistic reactions, which may increase the pain and induce vicious circles. Since many clinicians and researchers nowadays notice that pain during VIC often starts at young age, it is important to investigate how pain during VIC starts and is maintained in younger populations. The overall aim of this thesis was to investigate young women’s experiences of ideal sexual situations and pain during VIC. Women aged 13-22 years participated in our studies, which used both quantitative (study I and IV) and qualitative (study II and III) methods. For paper I, a questionnaire was developed and used in a YC sample (n=300); informants for paper II were selected from that sample to participate in qualitative interviews (n=16). Another qualitative interview study for paper III with a complimentary research question was conducted in a different YC sample (n=14). For paper IV, a questionnaire was developed based on the results from study I, II and III to test the hypotheses derived from study II in a sample of female high school students (n=1566). The findings revealed that 65% of the women reported pain related to first VIC. Among those who reported VIC during the previous month, 49% had experienced pain and/or discomfort during VIC during that same period (paper I). In paper IV, 47% of the women reported experience of pain and/or discomfort during VIC, and among those, 47% continued to have VIC, 22% feigned enjoyment, and 33% omitted telling the partner about their pain. In paper II, the women’s reasons for continuing to have VIC despite pain were: striving to reach their ideal image of a woman, characterized as always willing to have VIC; being perceptive of their partner’s sexual needs; and being able to satisfy their partner. In paper IV the hypotheses derived from study II were confirmed and showed, for example that a significantly higher proportion of women who continue to have VIC despite pain than women who did not had difficulty refusing sex when the partner wants it, felt inferior to the partner during sex, regarded the partner’s satisfaction as more important than their own, felt dissatisfaction with their sex life, and feigned enjoyment despite pain. In a multivariate model, continuing to have VIC despite pain was associated with feelings of being inferior to the partner during sex (adjusted OR 1.82; CI 1.10-3.02), dissatisfaction with their own sex lives (adjusted OR 1.76; CI 1.14-2.72) and feigning enjoyment while having pain (adjusted OR 7.45; CI 4.37-12.69). The major reason for continuing to have VIC was that the partner’s enjoyment was prioritized higher than their own (paper IV). In paper III, we found that women without pain during VIC also felt pressure from social norms and demands and had experienced partners “driving their own race”. However, they managed to some extent to resist these unequal gender norms because of their urge to experience pleasure. In conclusion, pain during VIC is a common complaint among young Swedish women, and a high proportion of them continue having VIC despite pain. The women’s notion of prioritizing the partners´ enjoyment before their own illustrates that unequal gender regimes affect young women’s (hetero)sexuality negatively.
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Rizziolli, Elíris Cristina. ""Variedades de Thom-Boardman, ideais Jacobianos e singularidades de aplicações diferenciáveis"." Universidade de São Paulo, 2001. http://www.teses.usp.br/teses/disponiveis/55/55135/tde-27082003-095607/.
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Neste trabalho é desenvolvido um estudo sobre a relação entre as variedades de Thom-Boardman e os ideais jacobianos iterados associados a estas variedades. Inicialmente são estudadas as singularidades de Thom-Boardman associadas a germes de aplicações analíticas com a finalidade de introduzir as varidades de Thom-Boardman no espaço dos jatos. Posteriormente são estudados os ideais jacobianos extendidos, seguindo a construção de Morin. Finalmente é definida a multiplicidade c_i(f) associada a um símbolo de Boardman i=(i_1,...,i_k) e ao extrato (Sigma)^1(f).<br>In this work we study the relation between the Thom-Boardman manifolds and the iterated jacobian ideals associate to these manifolds. First, we study the Thom-Boardman singularities associate to analitic map germs with the objective to introduce Thom-Boardman manifolds in the jet space. After, we study the extended jacobians ideals, following Morin's construction. We give the definition of the mulitiplicity c_i(f) associate to a Boadman symbol i=(i_1,...,i_k) and the stratum (Sigma)^i(f).
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Fernández, Sánchez Jesús. "On Sandwiched Surface Singularities and Complete Ideals." Doctoral thesis, Universitat de Barcelona, 2004. http://hdl.handle.net/10803/22643.
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The original interest in sandwiched singularities comes from a natural question posed by J. Nash in the early sixties to H. Hironaka: “Does a finite succession of Nash transformations or normalized Nash transformations resolve the singularities of a reduced algebraic variety?” In 1975, A. Nobile proved that, in characteristic zero, a Nash transformation is an isomorphism only in case the original variety is already non-singular. It turns out, in particular, that curve singularities are resolved by a succession of Nash transformations. Rebasoo proved in his Ph. D. thesis that Nash transformations also resolve certain kinds of quasi-homogeneous hypersurface singularities in (C)3. In 1982, G. Gonzalez-Sprinberg proved that normalized Nash transformations resolve rational double points and cyclic quotients singularities of surfaces. Then, H. Hironaka proved that after a finite succession of normalized Nash transformations one obtains a surface “X” which birationally dominates a non-singular surface. By definition, the singularities of “X” are sandwiched singularities. Some years later, M. Spivakovsky proves that sandwiched singularities are resolved by normalized Nash transformations, thus giving a positive answer to the original question posed by Nash for the case of surfaces over C.
Since then, a constant interest in sandwiched singularities has been shown, and they have been deeply studied from the point of view of deformation theory by de Jong and van Straten, and also by Stolen and Mohring. Sandwiched singularities have been also studied as a nice testing ground for the Nash and the wedge Problem by Lejeune-Jalabert and Reguera, where the main idea is to extend combinatorial arguments for toric surface singularities to sandwiched ones.
Sandwiched singularities are the singularities obtained by blowing-up a complete ideal in the local ring of a regular point on a surface. They are rational surface singularities (roughly speaking, isolated singularities whose resolution has no effect on the arithmetic genus of the surface) and among them are included all cyclic quotients and minimal surface singularities. Sandwiched singularities are Cohen-Macaulay, but are not complete intersections and in general, there are no simple equations for them. The purpose of this memoir is to study sandwiched singularities through their relationship to the infinitely near base points of the complete ideals blownup to obtain them.
Now, we briefly summarize the main contents of each one of the chapters. Chapter I is of preliminary nature and gives references to the literature for proofs. Concepts and well-known facts about infinitely near points, weighted clusters, complete ideals and rational and sandwiched surface singularities are reviewed and some consequences that are needed in the memoir are derived. In Chapter II we establish the main link between the study of sandwiched singularities and the theory of Enriques diagrams of weighted clusters and we derive some results on sandwiched singularities by using the unloading procedure.
Chapter III deals essentially with the principality of divisors going through a sandwiched singularity. It is well known that Wei divisors going through a singularity (X, Q) are not Cartier divisors in general.
In Chapter IV we use the results of Chapter III to explore the connection between the ideal sheaves on “X” with finite cosupport contained in the exceptional locus and the complete m(o)-primary ideals in R. Chapter V is devoted to derive consequences related to the Nash conjecture of arcs for sandwiched singularities.
In Appendix A, we provide the listings of three programs in language C implementing some of the algorithms proposed. These programs have been used to compute some of the examples presented throughout the memoir.
Part of the results of this thesis has been published or will be published in:
• J. Fernandez-Sanchez, On sandwiched singularities and complete ideals,
J. Pure Appl. Algebra 185 (2003), no. 1-3, 165-175. [19]
• J. Fernandez-Sanchez, Nash families of smooth arcs on a sandwiched
singularity, To appear in Math. Proc. Cambridge. Philos. Soc. [18]
• J. Fernandez-Sanchez, Equivalence of the Nash conjecture for primitive
and sandwiched singularities, To appear in Proc. Amer. Math.
Soc. [17]
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Nordgren, Björn. "Analysis of Value Ideals in Swedish Government Agency Electronic Archive projects : Value ideals in four electronic archive projects." Thesis, Mittuniversitetet, Institutionen för informationssystem och –teknologi, 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:miun:diva-42517.
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The values and motives behind e-Government projects are sometimes taken forgranted and are often considered as synchronised. Electronic archives can beconsidered a vital e-Government project, and the aim of this study was toinvestigate the values behind electronic archive projects for government agencies.This was achieved by investigating four different specifically chosen governmentagencies: three with electronic archives, and one without, and then assessing themusing the theoretical framework set out in Rose et al's article ’Managinge-Government’ published in Info Systems Journal in 2015: value position theory.The chosen government agencies were: Migrationsverket (the Swedish MigrationAgency), Skatteverket (the Swedish Tax Agency), Energimydigheten (the SwedishEnergy Agency), and Sveriges Geologiska Undersökning (Sweden’s GeologicalSurvey- SGU). Interviews were conducted with those archivists responsible for theelectronic archives at each of these four public agencies. The results of theinterviews were analysed using the value position theory. As a result, severaldifferent values were identified, though the values attached to professionality andefficiency ideals were more identifiable in the interviews than the values attachedto service and engagement. The values guiding the electronic archive projects werefound to be largely congruent. However, these values are not necessarilyrecognised on the state level, as shown by the fact that Statens Servicecenter’sproject has ended without result.
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Bengs, Carita. "Looking good : a study of gendered body ideals among young people." Doctoral thesis, Online version, 2000. http://bibpurl.oclc.org/web/24363.
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Šimkutė, Ieva. "Lieknumo idealai žiniasklaidoje: tarpkultūrinis aspektas." Master's thesis, Lithuanian Academic Libraries Network (LABT), 2014. http://vddb.library.lt/obj/LT-eLABa-0001:E.02~2011~D_20140701_164507-68905.
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Magistro darbo objektas – lieknumo idealai žiniasklaidoje. Darbo tikslas - išanalizuoti skirtingų šalių visuomenėse ir žiniasklaidoje egzistuojančius lieknumo idealus. Darbo uždaviniai: aptarti teorijas, aiškinančias žiniasklaidos įtaką mitybai; išanalizuoti tarpinius žiniasklaidos poveikio kintamuosius bei žiniasklaidoje poveikį švelninančius veiksnius; apžvelgti istorinę lieknumo idealų raidą; išanalizuoti lieknumo idealus, egzistuojančius skirtingose visuomenėse šiandieniniame pasaulyje; išanalizuoti lieknumo idealus, propaguojamus žiniasklaidoje; atlikti lieknumo idealų, propaguojamų lietuviškuose serialuose, tyrimą; atlikti palyginamąją lieknumo idealų propaguojamų Lietuvos televizijų ir užsienio šalių serialuose analizę. Išnagrinėjus mokslinę literatūrą, išskirtos teorijos (socialinio lyginimo, kultivacijos ir t.t.) aiškinančios žiniasklaidos poveikį mitybai bei nustatyta, kad nė viena iš jų nėra pajėgi savarankiškai paaiškinti žiniasklaidos poveikio mitybai ir lieknumo idealui mechanizmo. Taip pat nustatyti tarpiniai žiniasklaidos poveikio kintamieji, galintys skatinti arba švelninti žiniasklaidos poveikį, bei žiniasklaidos poveikį švelninantys veiksniai. Išnagrinėjus istorinę lieknumo idealų raidą nustatyta, kad skirtingu laikotarpiu egzistavo skirtingi grožio bei lieknumo standartai, kuriems būdinga cikliška kaita. Taip pat nustatyta, kad net ir šiandieniniame pasaulyje skirtingose kultūrose egzistuoja skirtingi moterų bei vyrų lieknumo idealai. Išskirti svarbiausi... [toliau žr. visą tekstą]<br>Object: body image ideals in the media. Objective: to analyze body image ideals prevailing in different countries. Tasks: review theories, contributing to explanation of media‘s influence on one‘s eating behavior; analyze the moderators and mitigating factors of media‘s influence; review the historical development of body image ideals; analyze modern body image ideals prevailing in different societies; analyze body image ideals in the media; research body image ideals, prevailing in the Lithuanian TV series; compare body image ideals, prevailing in Lithuanian and foreign country’s TV series. Methods: analysis and generalization of related literature; quantitative content analysis of body image ideals portrayed in Lithuanian TV series; comparative analysis of body image ideals portrayed in Lithuanian and USA TV series. Having analyzed the wide scope of science literature, theories contributing to explanation of media’s influence on eating behavior were abstracted, and the conclusion that neither of them is capable of giving the complete explanation of the media’s influence on one’s eating behavior process was drawn. It is only explicit that media does influence our self-esteem and eating behavior as a result. Also, moderators capable of either mitigating or intensifying medias influence were pointed out, as well as mitigating factors, that can be used for reducing negative media influence on eating behavior. Review of the body image ideals throughout the history revealed... [to full text]
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Taekema, Sanne. "The concept of ideals in legal theory /." The Hague : Kluwer Law International, 2003. http://opac.nebis.ch/cgi-bin/showAbstract.pl?u20=904111971X.
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