Relevant bibliographies by topics / Commutative ring / Dissertations / Theses
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Dissertations / Theses on the topic 'Commutative ring'

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Published: 4 June 2021
Last updated: 25 July 2025

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1

Duncan, A. J. "Two topics in commutative ring theory." Thesis, University of Edinburgh, 1988. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.234124.

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2

Hedenlund, Alice. "Galois Theory of Commutative Ring Spectra." Thesis, KTH, Matematik (Avd.), 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-183512.

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This thesis discusses Galois theory of ring spectra in the sense of John Rognes. The aim is to give a clear introduction that provides a solid foundation for further studies into the subject. We introduce ring spectra using the symmetric spectra of Hovey, Shipley and Smith, and discuss the symmetric monoidal model structure on this category. We define and give results for Galois extensions of these objects. We also give examples involving Eilenberg-Mac Lane spectra of commutative rings, topological K-theory spectra and cochain algebras of these. Galois extensions of ring spectra are compared to
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3

Hasse, Erik Gregory. "Lowest terms in commutative rings." Diss., University of Iowa, 2018. https://ir.uiowa.edu/etd/6433.

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Putting fractions in lowest terms is a common problem for basic algebra courses, but it is rarely discussed in abstract algebra. In a 1990 paper, D.D. Anderson, D.F. Anderson, and M. Zafrullah published a paper called Factorization in Integral Domains, which summarized the results concerning different factorization properties in domains. In it, they defined an LT domain as one where every fraction is equal to a fraction in lowest terms. That is, for any x/y in the field of fractions of D, there is some a/b with x/y=a/b and the greatest common divisor of a and b is 1. In addition, R. Gilmer inc
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4

Stalvey, Harrison. "Weak Primary Decomposition of Modules Over a Commutative Ring." Digital Archive @ GSU, 2010. http://digitalarchive.gsu.edu/math_theses/84.

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This paper presents the theory of weak primary decomposition of modules over a commutative ring. A generalization of the classic well-known theory of primary decomposition, weak primary decomposition is a consequence of the notions of weakly associated prime ideals and nearly nilpotent elements, which were introduced by N. Bourbaki. We begin by discussing basic facts about classic primary decomposition. Then we prove the results on weak primary decomposition, which are parallel to the classic case. Lastly, we define and generalize the Compatibility property of primary decomposition.
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5

Alshaniafi, Y. S. "The homological grade of a module over a commutative ring." Thesis, University of Southampton, 1990. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.280830.

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6

Baig, Muslim. "Primary Decomposition and Secondary Representation of Modules over a Commutative Ring." Digital Archive @ GSU, 2009. http://digitalarchive.gsu.edu/math_theses/69.

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This paper presents the theory of Secondary Representation of modules over a commutative ring and their Attached Primes; introduced in 1973 by I. MacDonald as a dual to the important theory of associated primes and primary decomposition in commutative algebra. The paper explores many of the basic aspects of the theory of primary decomposition and associated primes of modules in the hopes to delineate and motivate the construction of a secondary representation, when possible. The thesis discusses the results of the uniqueness of representable modules and their attached primes, and, in particula
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7

Martini, Lorenzo. "Local coherence of hearts in the derived category of a commutative ring." Doctoral thesis, Università degli studi di Trento, 2022. http://hdl.handle.net/11572/354322.

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Approximation theory is a fundamental tool in order to study the representation theory of a ring R. Roughly speaking, it consists in determining suitable additive or abelian subcategories of the whole module category Mod-R with nice enough functorial properties. For example, torsion theory is a well suited incarnation of approximation theory. Of course, such an idea has been generalised to the additive setting itself, so that both Mod-R and other interesting categories related with R may be linked functorially. By the seminal work of Beilinson, Bernstein and Deligne (1982), the derived categor
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8

Philippoussis, Anthony. "Necessary and sufficient conditions so that a commutative ring can be embedded into a strongly [pi]-regular ring." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1998. http://www.collectionscanada.ca/obj/s4/f2/dsk2/tape15/PQDD_0007/MQ39934.pdf.

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9

Edmonds, Ranthony A. C. "Factorization in polynomial rings with zero divisors." Diss., University of Iowa, 2018. https://ir.uiowa.edu/etd/3248.

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Factorization theory is concerned with the decomposition of mathematical objects. Such an object could be a polynomial, a number in the set of integers, or more generally an element in a ring. A classic example of a ring is the set of integers. If we take any two integers, for example 2 and 3, we know that $2 \cdot 3=3\cdot 2$, which shows that multiplication is commutative. Thus, the integers are a commutative ring. Also, if we take any two integers, call them $a$ and $b$, and their product $a\cdot b=0$, we know that $a$ or $b$ must be $0$. Any ring that possesses this property is called an i
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10

Oyinsan, Sola. "Primary decomposition of ideals in a ring." CSUSB ScholarWorks, 2007. https://scholarworks.lib.csusb.edu/etd-project/3289.

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The concept of unique factorization was first recognized in the 1840s, but even then, it was still fairly believed to be automatic. The error of this assumption was exposed largely through attempts to prove Pierre de Fermat's, 1601-1665, last theorem. Once mathematicians discovered that this property did not always hold, it was only natural for them to try to search for the strongest available alternative. Thus began the attempt to generalize unique factorization. Using the ascending chain condition on principle ideals, we will show the conditions under which a ring is a unique factorization d
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11

Nossem, Nicole. "On the perfect closure of a commutative Noetherian ring of positive prime characteristic." Thesis, University of Sheffield, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.251466.

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12

Crawford, Simon Philip. "Singularities of noncommutative surfaces." Thesis, University of Edinburgh, 2018. http://hdl.handle.net/1842/31543.

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The primary objects of study in this thesis are noncommutative surfaces; that is, noncommutative noetherian domains of GK dimension 2. Frequently these rings will also be singular, in the sense that they have infinite global dimension. Very little is known about singularities of noncommutative rings, particularly those which are not finite over their centre. In this thesis, we are able to give a precise description of the singularities of a few families of examples. In many examples, we lay the foundations of noncommutative singularity theory by giving a precise description of the singularitie
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13

Race, Denise T. (Denise Tatsch). "Containment Relations Between Classes of Regular Ideals in a Ring with Few Zero Divisors." Thesis, North Texas State University, 1987. https://digital.library.unt.edu/ark:/67531/metadc331394/.

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This dissertation focuses on the significance of containment relations between the above mentioned classes of ideals. The main problem considered in Chapter II is determining conditions which lead a ring to be a P-ring, D-ring, or AM-ring when every regular ideal is a P-ideal, D-ideal, or AM-ideal, respectively. We also consider containment relations between classes of regular ideals which guarantee that the ring is a quasi-valuation ring. We continue this study into the third chapter; in particular, we look at the conditions in a quasi-valuation ring which lead to a = Jr, sr - f, and a = v. F
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14

Mbirika, Abukuse III. "Analysis of symmetric function ideals: towards a combinatorial description of the cohomology ring of Hessenberg varieties." Diss., University of Iowa, 2010. https://ir.uiowa.edu/etd/708.

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Symmetric functions arise in many areas of mathematics including combinatorics, topology and algebraic geometry. Using ideals of symmetric functions, we tie these three branches together. This thesis generalizes work of Garsia and Procesi in 1992 that gave a quotient ring presentation for the cohomology ring of Springer varieties. Let R be the polynomial ring Ζ[x1,…,xn]. We present two different ideals in R. Both are parametrized by a Hessenberg function h, namely a nondecreasing function that satisfies h(i) ≥ i for all i. The first ideal, which we call Ih, is generated by modified elementary
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15

Di, Lorenzo Andrea. "Integral Chow ring and cohomological invariants of stacks of hyperelliptic curves." Doctoral thesis, Scuola Normale Superiore, 2019. http://hdl.handle.net/11384/85744.

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16

Steward, Michael. "Extending the Skolem Property." The Ohio State University, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=osu1492517341492202.

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17

Tête, Claire. "Profondeur, dimension et résolutions en algèbre commutative : quelques aspects effectifs." Thesis, Poitiers, 2014. http://www.theses.fr/2014POIT2288/document.

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Cette thèse d'algèbre commutative porte principalement sur la théorie de la profondeur. Nous nous efforçons d'en fournir une approche épurée d'hypothèse noethérienne dans l'espoir d'échapper aux idéaux premiers et ceci afin de manier des objets élémentaires et explicites. Parmi ces objets, figurent les complexes algébriques de Koszul et de Cech dont nous étudions les propriétés cohomologiques grâce à des résultats simples portant sur la cohomologie du totalisé d'un bicomplexe. Dans le cadre de la cohomologie de Cech, nous avons établi la longue suite exacte de Mayer-Vietoris avec un traitement
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18

Margolin, Benjamin Paul. "Non-commutative deformation rings." Diss., University of Iowa, 2016. https://ir.uiowa.edu/etd/3135.

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The goal of this thesis is to study non-commutative deformation rings of representations of algebras. The main motivation is to provide a generalization of the deformation theory over commutative local rings studied by B. Mazur, M. Schlessinger and others. The latter deformation theory has played an important role in number theory, and in particular in the proof of Fermat's Last Theorem. The thesis is divided into two parts. In the first part, A is an arbitrary λ-algebra for a complete local commutative Noetherian ring λ with residue field k. A category Ĉ is defined whose objects are complete
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19

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 variou
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20

Rumbos, Irma Beatriz. "A sheaf representation for non-commutative rings /." Thesis, McGill University, 1987. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=70356.

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For any ring R (associative with 1) we associate a space X of prime torsion theories endowed with Golan's SBO-topology. A separated presheaf L(-,M) on X is then constructed for any right R-module M$ sb{ rm R}$, and a sufficient condition on M is given such that L(-,M) is actually a sheaf. The sheaf space rm E { buildrel{ rm p} over longrightarrow} X) etermined by L(-,M) represents M in the following sense: M is isomorphic to the module of continuous global sections of p. These results are applied to the right R-module R$ sb{ rm R}$ and it is seen that semiprime rings satisfy the required cond
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21

Vo, Monika. "New classes of finite commutative rings." Thesis, University of Hawaii at Manoa, 2003. http://proquest.umi.com/pqdweb?index=2&did=765961151&SrchMode=1&sid=1&Fmt=2&VInst=PROD&VType=PQD&RQT=309&VName=PQD&TS=1208558919&clientId=23440.

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22

Akalan, Evrim. "Generalizations of non-commutative uniquefactorization rings." Thesis, University of Warwick, 2008. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.502119.

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There is a well-developed theory of unique factorization domains in commutative algebra. The generalization of this concept to non-commutative rings has also been extensively studied (e.g. in [19], [16], [1]). This thesis is concerned with classes of non-commutative rings which are generalizations of non-commutative Noetherian unique factorization rings. Noetherian UFR's are maximal orders and every reflexive ideal is invertible in these rings. Clearly maximal orders and reflexive ideals are important concepts and we examine them in this thesis. UFR's can also be considered as rings in which t
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23

Denizler, Ismail Hakki. "Artinian modules over commutative rings, and duality." Thesis, University of Sheffield, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.364185.

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24

Granger, Ginger Thibodeaux. "Properties of R-Modules." Thesis, University of North Texas, 1989. https://digital.library.unt.edu/ark:/67531/metadc500710/.

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This thesis investigates some of the properties of R-modules. The material is presented in three chapters. Definitions and theorems which are assumed are stated in Chapter I. Proofs of these theorems may be found in Zariski and Samuel, Commutative Algebra, Vol. I, 1958. It is assumed that the reader is familiar with the basic properties of commutative rings and ideals in rings. Properties of R-modules are developed in Chapter II. The most important results presented in this chapter include existence theorems for R-modules and properties of submodules in R-modules. The third and final chapter p
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25

Mooney, Christopher Park. "Generalized factorization in commutative rings with zero-divisors." Thesis, The University of Iowa, 2013. http://pqdtopen.proquest.com/#viewpdf?dispub=3595128.

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<p> The study of factorization in integral domains has a long history. Unique factorization domains, like the integers, have been studied extensively for many years. More recently, mathematicians have turned their attention to generalizations of this such as Dedekind domains or other domains which have weaker factorization properties. Many authors have sought to generalize the notion of factorization in domains. One particular method which has encapsulated many of the generalizations into a single study is that of &tau;-factorization, studied extensively by A. Frazier and D.D. Anderson. <
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26

Coutinho, S. C. "Generating modules efficiently over non-commutative noetherian rings." Thesis, University of Leeds, 1986. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.372589.

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27

Hayes, Leslie Danielle. "The plus closure of an ideal." Access restricted to users with UT Austin EID Full text (PDF) from UMI/Dissertation Abstracts International, 2001. http://wwwlib.umi.com/cr/utexas/fullcit?p3035948.

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28

Emerson, Sharon Sue. "Overrings of an Integral Domain." Thesis, University of North Texas, 1992. https://digital.library.unt.edu/ark:/67531/metadc332679/.

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This dissertation focuses on the properties of a domain which has the property that each ideal is a finite intersection of a π-ideal, the properties of a domain which have the property that each ideal is a finite product of π-ideal, and the containment relations of the resulting classes of ideals. Chapter 1 states definitions which are needed in later chapters. Chapters 2 and 3 focuses on domains which have the property that each ideal in D is a finite intersection of π-ideals while Chapter 4 focuses on domains with the property that each ideal is a finite product of π-ideals. Chapter 5 discus
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29

Volkweis, Leite Samuel [Verfasser]. "p-adic Representations of Commutative Rings / Samuel Volkweis Leite." Konstanz : Bibliothek der Universität Konstanz, 2013. http://d-nb.info/1031879943/34.

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30

Bell, Kathleen. "Cayley Graphs of PSL(2) over Finite Commutative Rings." TopSCHOLAR®, 2018. https://digitalcommons.wku.edu/theses/2102.

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Hadwiger's conjecture is one of the deepest open questions in graph theory, and Cayley graphs are an applicable and useful subtopic of algebra. Chapter 1 will introduce Hadwiger's conjecture and Cayley graphs, providing a summary of background information on those topics, and continuing by introducing our problem. Chapter 2 will provide necessary definitions. Chapter 3 will give a brief survey of background information and of the existing literature on Hadwiger's conjecture, Hamiltonicity, and the isoperimetric number; in this chapter we will explore what cases are already shown and what the m
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31

Ugolini, Matteo. "K3 surfaces." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2019. http://amslaurea.unibo.it/18774/.

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32

Chattopadhyay, Arkadev. "Circuits, communication and polynomials." Thesis, McGill University, 2008. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=115660.

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In this thesis, we prove unconditional lower bounds on resources needed to compute explicit functions in the following three models of computation: constant-depth boolean circuits, multivariate polynomials over commutative rings and the 'Number on the Forehead' model of multiparty communication. Apart from using tools from diverse areas, we exploit the rich interplay between these models to make progress on questions arising in the study of each of them.<br>Boolean circuits are natural computing devices and are ubiquitous in the modern electronic age. We study the limitation of this model when
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33

Oman, Gregory Grant. "A generalization of Jónsson modules over commutative rings with identity." Columbus, Ohio : Ohio State University, 2006. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1164331653.

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34

Bradford, Jeremy. "Commutative endomorphism rings of simple abelian varieties over finite fields." Thesis, University of Maryland, College Park, 2013. http://pqdtopen.proquest.com/#viewpdf?dispub=3557641.

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<p>In this thesis we look at simple abelian varieties defined over a finite field <i>k</i> = [special characters omitted]<i><sub>p</sub>n</i> with End<i><sub>k</sub></i>(<i> A</i>) commutative. We derive a formula that connects the <i>p </i>-rank <i>r(A)</i> with the splitting behavior of <i> p</i> in <i>E</i> = [special characters omitted](&pi;), where &pi; is a root of the characteristic polynomial of the Frobenius endomorphism. We show how this formula can be used to explicitly list all possible splitting behaviors of <i>p</i> in [special characters omitted]<i><sub>E</sub></i>, and we do
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35

Oman, Gregory Grant. "A generalization of Jónsson modules over commutative rings with identity." The Ohio State University, 2006. http://rave.ohiolink.edu/etdc/view?acc_num=osu1164331653.

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36

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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37

Trentham, Stacy Michelle. "Atomicity in Rings with Zero Divisors." Diss., North Dakota State University, 2011. https://hdl.handle.net/10365/28905.

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In this dissertation, we examine atomicity in rings with zero divisions. We begin by examining the relationship between a ring’s level of atomicity and the highest level of irreducibility shared by the ring’s irreducible elements. Later, we chose one of the higher forms of atomicity and identify ways of building large classes of examples of rings that rise to this level of atomicity but no higher. Characteristics of the various types of irreducible elements will also be examined. Next, we extend our view to include polynomial extensions of rings with zero divisors. In particular, we focus on p
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38

Trentham, William Travis. "Applications of Groups of Divisibility and a Generalization of Krull Dimension." Diss., North Dakota State University, 2011. https://hdl.handle.net/10365/28904.

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Groups of divisibility have played an important role in commutative algebra for many years. In 1932 Wolfgang Krull showed in [12] that every linearly ordered Abelian group can be realized as the group of divisibility of a valuation domain. Since then it has also been proven that every lattice-ordered Abelian group can be recognized as the group of divisibility of a Bezont domain. Knowing these two facts allows us to use groups of divisibility to find examples of rings with highly exotic properties. For instance, we use them here to find examples of rings which admit elements that factor unique
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39

Reinkoester, Jeremiah N. "Relative primeness." Diss., University of Iowa, 2010. https://ir.uiowa.edu/etd/585.

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In [2], Dan Anderson and Andrea Frazier introduced a generalized theory of factorization. Given a relation τ on the nonzero, nonunit elements of an integral domain D, they defined a τ-factorization of a to be any proper factorization a = λa1 · · · an where λ is in U (D) and ai is τ-related to aj, denoted ai τ aj, for i not equal to j . From here they developed an abstract theory of factorization that generalized factorization in the usual sense. They were able to develop a number of results analogous to results already known for usual factorization. Our work focuses on the notion of τ-factoriz
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40

Nachar, Georges. "Caténarité et anneaux de séries formelles." Lyon 1, 1985. http://www.theses.fr/1985LYO11673.

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Soient r un anneau commutatif de dimension de krull finie et k son corps des fractions. On note r(x) (resp. R((x))) l'anneau des polynomes (resp. Des series formelles) en x sur r. J. T. Arnold (1) a montre que si r n'est pas un sft-anneau alors dim r((x))=infini. De plus, si d est un sft-anneau prueferien, dim d((x::(1),. . . ,x::(n)))=n dim d+1. D'autre part, pour un anneau noetherien d, dim d((x::(1),. . . ,x::(n)))= dim d+n. S. Doering et y. Lequain ont montre que les proprietes suivantes sont equivalentes : a) d(x::(1),. . . ,x::(n)) est catenaire; b) d((x::(1),. . . ,x::(n))) est catenair
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41

Green, Ellen Yvonne. "Characterizing the strong two-generators of certain Noetherian domains." CSUSB ScholarWorks, 1997. https://scholarworks.lib.csusb.edu/etd-project/1539.

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42

Petin, Burkhard. "Ein kombinatorisches Beweisverfahren für produktrelationen zwischen Gauss-summen über endlichen kommutativen Ringen." Bonn : [s.n.], 1990. http://catalog.hathitrust.org/api/volumes/oclc/24807249.html.

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43

Malec, Sara. "Intersection Algebras and Pointed Rational Cones." Digital Archive @ GSU, 2013. http://digitalarchive.gsu.edu/math_diss/14.

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In this dissertation we study the algebraic properties of the intersection algebra of two ideals I and J in a Noetherian ring R. A major part of the dissertation is devoted to the finite generation of these algebras and developing methods of obtaining their generators when the algebra is finitely generated. We prove that the intersection algebra is a finitely generated R-algebra when R is a Unique Factorization Domain and the two ideals are principal, and use fans of cones to find the algebra generators. This is done in Chapter 2, which concludes with introducing a new class of algebras called
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44

Chaitou, Mohamad. "Performance of multicast packet aggregation with quality of service support in all-optical packet-switched ring networks." Evry, Institut national des télécommunications, 2006. http://www.theses.fr/2006TELE0007.

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La technologie optique WDM (Wavelength Division Multiplexing) subit un grand succès grâce aux besoins croissants en debit du traffic basé sur le protocole IP (Inter- net Protocol). Une solution efficace pour l'adaptation du traffic IP au niveau WDM dans les reseaux metropolitains optiques (Metropolitan Area Networks-MANs) consiste µa l'utilisation de la commutation de paquets optiques (Optical Packet Switching-OPS), basee sur le multiplexage statistique des paquets optiques de taille fixe dans un environnement synchrone. Ce travail presente un nouveau mecanisme effcace pour supporter directeme
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45

Zagrodny, Christopher Michael. "Algebraic Concepts in the Study of Graphs and Simplicial Complexes." Digital Archive @ GSU, 2006. http://digitalarchive.gsu.edu/math_theses/7.

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This paper presents a survey of concepts in commutative algebra that have applications to topology and graph theory. The primary algebraic focus will be on Stanley-Reisner rings, classes of polynomial rings that can describe simplicial complexes. Stanley-Reisner rings are defined via square-free monomial ideals. The paper will present many aspects of the theory of these ideals and discuss how they relate to important constructions in commutative algebra, such as finite generation of ideals, graded rings and modules, localization and associated primes, primary decomposition of ideals and Hilber
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46

Byun, Eui Won James. "Affine varieties, Groebner basis, and applications." CSUSB ScholarWorks, 2000. https://scholarworks.lib.csusb.edu/etd-project/1611.

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47

Salt, Brittney M. "MONOID RINGS AND STRONGLY TWO-GENERATED IDEALS." CSUSB ScholarWorks, 2014. https://scholarworks.lib.csusb.edu/etd/31.

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This paper determines whether monoid rings with the two-generator property have the strong two-generator property. Dedekind domains have both the two-generator and strong two-generator properties. How common is this? Two cases are considered here: the zero-dimensional case and the one-dimensional case for monoid rings. Each case is looked at to determine if monoid rings that are not PIRs but are two-generated have the strong two-generator property. Full results are given in the zero-dimensional case, however only partial results have been found for the one-dimensional case.
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48

Le, Gros Giovanna. "Minimal approximations for cotorsion pairs generated by modules of projective dimension at most one over commutative rings." Doctoral thesis, Università degli studi di Padova, 2019. http://hdl.handle.net/11577/3423180.

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In this thesis we study cotorsion pairs (A, B) generated by classes of R-modules of projective dimension at most one. We are interested in when these cotorsion pairs provide covers or envelopes over commutative rings. More precisely, we investigate Enochs' Conjecture in this setting. That is, for a class A contained in the class of modules of projective dimension at most one, denoted P_1, we investigate the question of whether A is covering necessarily implies that A is closed under direct limits. Additionally, under certain restrictions we characterise the rings which satisfy this property. T
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Diaz, Noguera Maribel del Carmen. "Sobre derivações localmente nilpotentes dos aneis K[x,y,z] e K[x,y]." [s.n.], 2007. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306307.

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Orientador: Paulo Roberto Brumatti<br>Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Ciencia da Computação<br>Made available in DSpace on 2018-08-09T23:37:45Z (GMT). No. of bitstreams: 1 DiazNoguera_MaribeldelCarmen_M.pdf: 632573 bytes, checksum: fbcf2bd0092558fce4ba4d082d4c68c7 (MD5) Previous issue date: 2007<br>Resumo: O principal objetivo desta dissertação é apresentar resultados centrais sobre derivações localmente nilpotentes no anel de polinômios B = k[x1, ..., xn], para n = 3 que foram apresentados por Daniel Daigle em [2 ], [3] e [4
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50

Gokhale, Dhananjay R. "Resolutions mod I, Golod pairs." Diss., Virginia Tech, 1992. http://hdl.handle.net/10919/39431.

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Let <i>R</i> be a commutative ring, <i>I</i> be an ideal in <i>R</i> and let <i>M</i> be a <i>R/ I</i> -module. In this thesis we construct a <i>R/ I</i> -projective resolution of <i>M</i> using given <i>R</i>-projective resolutions of <i>M</i> and <i>I</i>. As immediate consequences of our construction we give descriptions of the canonical maps Ext<sub>R/I</sub><i>(M,N)</i> -> Ext<sub>R</sub><i>(M,N)</i> and Tor<sup>R</sup><sub>N</sub><i>(M, N)</i> -> Tor<sup>R/I</sup><sub>n</sub><i>(M, N)</i> for a <i>R/I</i> module <i>N</i> and we give a new proof of a theorem of Gulliksen [6] which states
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