Dissertations / Theses: 'Modules (Algebra)'

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Burton, Cynthia L. "Hopf algebras and Dieudonné modules /." Thesis, Connect to this title online; UW restricted, 1998. http://hdl.handle.net/1773/5808.

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Kremer, Raymond Edward. "HOMOLOGICAL ALGEBRA WITH FILTERED MODULES." UKnowledge, 2014. http://uknowledge.uky.edu/math_etds/18.

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Classical homological algebra is done in a category of modules beginning with the study of projective and injective modules. This dissertation investigates analogous notions of projectivity and injectivity in a category of filtered modules. This category is similar to one studied by Sjödin, Nǎstǎsescu, and Van Oystaeyen. In particular, projective and injective objects with respect to the restricted class of strict morphisms are defined and characterized. Additionally, an analogue to the injective envelope is discussed with examples showing how this differs from the usual notion of an injective envelope.

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Jegan, Mahadevan. "Homomorphisms between bubble algebra modules." Thesis, City University London, 2013. http://openaccess.city.ac.uk/2380/.

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In this thesis, we study the representation theory of the bubble algebras. We focus on determining the homomorphisms between cell modules for these algebras. We show that the bubble algebras are cellular, and form a tower of recollement. By decomposing Gram matrices we are able to determine homomorphisms in the one arc case. We determine a generating set for the algebra (and its cardinality), and use this with a hypercuboid approach to determine homomorphisms in the general case. We end with a conjectural alternative approach to the general case involving matrix methods.

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Boukhobza, Mustapha. "Isométries de modules quadratiques." Lyon 1, 1987. http://www.theses.fr/1987LYO11744.

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Soient a un anneau integre dans lequel 2 est inversible, s une partie multiplicative de a, r = s**(-1)a et (m,q), (m',q') deux a-modules quadratiques reguliers de rang n isometriques sur r. On se propose de donner des conditions suffisantes pour qu'ils soient isometriques sur a. Une reponse positive a ete donne (7) quand a est normal et n=1. Pour n1, la reponse est en general negative; neanmoins, sur un anneau principal a, deux a-modules quadratiques isotropes sont isometriques sur a si et seulement si ils le sont sur r (ii. 4. 3), de meme, avec certaines hypotheses supplementaires, on montre des resultats analogues (ii. 5. 5) et (ii. 5. 9). Dans les demonstrations, on utilise essentiellement la technique du diagramme cartesien qui est apparue, sous diverses formes, dans les travaux de plusieurs auteurs (16), (17) et (20). Le premier chapitre de ce travail est consacre a divers rappels relatifs aux anneaux topologiques et a la completion d'un anneau respectant la topologie definie par un ideal de l'anneau; on s'interesse surtout aux proprietes particulieres de la completion permettant d'appliquer la technique du diagramme cartesien a notre etude. Le chapitre ii est consacre a l'etude du groupe orthogonal du module quadratique (m,q) orthogonal m(a), que l'on note q orthogonal h, sur un anneau principal. On demontre un resultat crucial : o::(ap)(q orthogonal h) = o::(a)(q orthogonal h). O::(ap)(q orthogonal h). La derniere partie de ce chapitre est l'aboutissement des notions etudiees precedemment; on demontre plus precisement que l'on peut repondre d'une maniere positive a notre probleme dans les cas suivants : (ii. 4. 3), (ii. 4. 4), (ii. 5. 5) et (ii. 5. 9). Dans le dernier chapitre, on caracterise le groupe orthogonal d'un module quadratique diagonal de rang 2, a::(1),a::(2), sur un anneau principal et on prouve que l'on peut simplifier : a::(1),a::(2) orthogonal (m,q)->(m',q') orthogonal (m,q) si (-1) n'est pas un carre dans chaque corps re- a/::(p. A) ou p est un element premier de a; ce resultat est ameliore dans le cas des anneaux de fractions de z (iii. 2. 3), on donne un contre-exemple (iii. 2. 4) montrant que la simplication n'est pas possible si le module quadratique diagonal de rang 2 est de la forme : a::(1),a::(2) ou a::(1) non= a::(2) mod u(a**(2)); ainsi notre resultat est, dans un certain sens, le meilleur possible

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Anderson, Benjamin John. "NAK for Ext, Ascent of Module Structures, and the Blindness of Extended Modules." Diss., North Dakota State University, 2012. https://hdl.handle.net/10365/26523.

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This dissertation investigates the interplay between properties of Ext modules and ascent of module structures along ring homomorphisms. First, we consider a flat local ring homomorphism ϕ: (R, [special characters omitted], k) → (S, [special characters omitted]S, k). We show that if M is a finitely generated R-module such that [special characters omitted](S, M) satisfies NAK (e.g. if [special characters omitted](S, M) is finitely generated over S) for i = 1,…, dimR( M), then [special characters omitted](S, M) = 0 for all i ≠ 0 and M has an S-module structure via ϕ. We also provide explicit computations of [special characters omitted](S, M) to indicate how large it can be when M does not have a compatible S-module structure. Next, we consider the properties of an R-module M that has a compatible S-module structure via the flat local ring homomorphism ϕ. Our results in this direction show that M cannot see the difference between the rings R and S. Specifically, many homological invariants of M are the same when computed over R and over S. Finally, we investigate these ideas in the non-local setting. We consider a faithfully flat ring homomorphism ϕ: R → S such that for all [special characters omitted] ∈ m-Spec R, the map R/[special characters omitted] → S/[special characters omitted]S is an isomorphism and the induced map ϕ*: Spec( S) → Spec(R) is such that ϕ*(m-Spec( S)) ⊆ m-Spec(R), and show that if M is a finitely generated R-module such that [special characters omitted](S, M) satisfies NAK for i = 1,…,dim R(M), then M has an S-module structure via ϕ, and obtain the same Ext vanishing as in the local case.

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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 presents an example which illustrates how a ring R, may be regarded as an R-module and speaks of the direct sum of ideals of a ring as a direct sum of submodules.

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Menemen, Filiz Alizde Rarail. "Confinitely amply weakly supplemented modules./." [s.l.]: [s.n.], 2005. http://library.iyte.edu.tr/tezler/master/matematik/T000389.pdf.

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Thesis (Master)--İzmir Institute of Technology, İzmir, 2005
Keywords:Supplemented modules, cofinitely supplemented modules, cofinitely amply supplemented modules, cofinitely amply weakly supplemented modules. Includes bibliographical references (leaves 23).

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Nguyen, Khanh Tung. "Cyclically presented modules, automorphism-invariant modules and poor modules." Doctoral thesis, Università degli studi di Padova, 2015. http://hdl.handle.net/11577/3423961.

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In this thesis, we study three kinds of modules: cyclically presented modules in relation to factorization of elements in a noncommutative integral domain, automorphism-invariant modules and poor modules. First, we investigate projective covers of cyclically presented modules, characterizing the rings over which every cyclically presented module has a projective cover. Such rings R are Von Neumann regular modulo their Jacobson radical J (R) and their idempotents can be lifted modulo J (R) . Then we study the modules M R whose endomorphism ring E := (MR) is Von Neumann regular modulo J (E) and their idempotents lift modulo J (E). Next, the endomorphism rings of automorphism-invariant modules and their injective envelopes are investigated. We consider some cases where automorphism-invariant modules are quasi-injective and a connection between automorphism-invariant modules and boolean rings. Finally, we give some necessary conditions for rings over which every non-zero cyclic module is poor.
In questa tesi studiamo tre tipi di moduli: i moduli ciclicamente presentati in relazione alla fattorizzazione degli elementi di un dominio di integrità non commutativo, i moduli automorphism-invariant e i moduli poveri. Innanzitutto studiamo i ricoprimenti proiettivi dei moduli ciclicamente presentati, caratterizzando gli anelli sui quali ogni modulo ciclicamente presentato ha un ricoprimento proiettivo. Tali anelli R sono regolari alla Von Neumann modulo il loro radicale di Jacobson J (R) e i loro idempotenti si sollevano modulo J (R). Poi studiamo i moduli M R il cui anello degli endomorfismi E := (MR) è regolare alla Von Neumann modulo J (R) e i loro idempotenti si sollevano modulo J (R). Studiamo quindi gli anelli degli endomorfismi dei moduli automorphism-invariant e i loro inviluppi iniettivi, consideriamo alcuni casi in cui i moduli automorphism-invariant sono quasi-iniettivi ed una relazione tra i moduli automorphism-invariant e gli anelli booleani. Infine diamo alcune condizioni necessarie per gli anelli sui quali ogni modulo ciclico è povero.

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Greene, Andrew Koichi. "Extensions of Hilbert modules over tensor algebras." Diss., University of Iowa, 2012. https://ir.uiowa.edu/etd/3309.

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This dissertation explores aspects of the representation theory for tensor algebras, which are non-selfadjoint operator algebras Muhly and Solel introduced in 1998, by developing a cohomology theory for completely bounded Hilbert modules. Similar theories have been developed for Banach modules by Johnson in 1970, for operator modules by Paulsen in 1997, and for Hilbert modules over the disc algebra by Carlson and Clark in 1995. The framework presented here was motivated by a desire to further understand the completely bounded representation theory for tensor algebras on Hilbert spaces. The focal point of this thesis is the first Ext group, Ext1, which is defined as equivalence classes of short exact sequences of completely bounded Hilbert modules. Alternate descriptions of this group are presented. For general operator algebras, Ext1 can be realized as the collection completely bounded derivations equivalent up to an inner derivation. When the operator algebra is a tensor algebra, Ext1 can be described as a quotient space of intertwining operators, a description analogous to a result of Ferguson in 1996 in the case of the classical disc algebra. A theorem of Sz.-Nagy and Foias from 1967, concerning contractions in triangular form, is applied to analyze derivations that are off-diagonal corners of completely contractive representations. It is proved that, in some cases, this analysis determines when all derivations must be inner or suggests ways to construct non-inner derivations. In the third chapter, a characterization is given of completely bounded representations of a tensor algebra in terms of similarities of contractive intertwiners. Also proven is that for a Csup*;-correspondence X over a Csup*;-algebra A and the Toeplitz algebra T(X), Mn(T(X))= T(Mn(X)). The analogous statement for tensor algebras is deduced as a corollary. In the final chapter, a brief survey of non-abelian category theory is provided. Extensions of completely bounded Hilbert modules over operator algebras are defined. Theorems asserting the projectivity of isometric modules and injectivity of coisometric modules by Carlson, Clark, Foias, and Williams in 1995 are generalized to the noncommutative setting of tensor algebras using commutant lifting. A result of Popesecu in 1996 for noncommutative disc algebras is also covered in the general framework of this thesis.

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Persson, Westin Elin. "Tilting modules in d-cluster tilting subcategories." Thesis, Uppsala universitet, Algebra och geometri, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-325539.

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11

Al-Hazmi, Husain Suleman S. "A study of CS and [sigma]-CS rings and modules." Ohio : Ohio University, 2005. http://www.ohiolink.edu/etd/view.cgi?ohiou112168376.

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12

Erdoğan, Sultan Eylem Alizade Refail. "Absolutely Supplement And Absolutely Complement Modules/." [s.l.]: [s.n.], 2004. http://library.iyte.edu.tr/tezler/master/matematik/T000339.pdf.

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13

Ssevviiri, David. "A contribution to the theory of prime modules." Thesis, Nelson Mandela Metropolitan University, 2013. http://hdl.handle.net/10948/d1019923.

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This thesis is aimed at generalizing notions of rings to modules. In par-ticular, notions of completely prime ideals, s-prime ideals, 2-primal rings and nilpotency of elements of rings are respectively generalized to completely prime submodules and classical completely prime submodules, s-prime submodules, 2-primal modules and nilpotency of elements of modules. Properties and rad-icals that arise from each of these notions are studied.

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14

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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15

Nilsson, Jonathan. "Simple Modules over Lie Algebras." Doctoral thesis, Uppsala universitet, Algebra och geometri, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-283061.

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Simple modules are the elemental components in representation theory for Lie algebras, and numerous mathematicians have worked on their construction and classification over the last century. This thesis consists of an introduction together with four research articles on the subject of simple Lie algebra modules. In the introduction we give a light treatment of the basic structure theory for simple finite dimensional complex Lie algebras and their representations. In particular we give a brief overview of the most well-known classes of Lie algebra modules: highest weight modules, cuspidal modules, Gelfand-Zetlin modules, Whittaker modules, and parabolically induced modules. The four papers contribute to the subject by construction and classification of new classes of Lie algebra modules. The first two papers focus on U(h)-free modules of rank 1 i.e. modules which are free of rank 1 when restricted to the enveloping algebra of the Cartan subalgebra. In Paper I we classify all such modules for the special linear Lie algebras sln+1(C), and we determine which of these modules are simple. For sl2 we also obtain some additional results on tensor product decomposition. Paper II uses the theory of coherent families to obtain a similar classification for U(h)-free modules over the symplectic Lie algebras sp2n(C). We also give a proof that U(h)-free modules do not exist for any other simple finite-dimensional algebras which completes the classification. In Paper III we construct a new large family of simple generalized Whittaker modules over the general linear Lie algebra gl2n(C). This family of modules is parametrized by non-singular nxn-matrices which makes it the second largest known family of gl2n-modules after the Gelfand-Zetlin modules. In Paper IV we obtain a new class of sln+2(C)-modules by applying the techniques of parabolic induction to the U(h)-free sln+1-modules we constructed in Paper I. We determine necessary and sufficient conditions for these parabolically induced modules to be simple.

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Turner, David P. "Coefficient space properties and a Schur algebra generalization." Auburn, Ala., 2005. http://repo.lib.auburn.edu/2005%20Fall/Dissertation/TURNER_DAVID_51.pdf.

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Lundkvist, Signe. "Torsion Classes and Support Tilting Modules for Path Algebras." Thesis, Uppsala universitet, Algebra och geometri, 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-355364.

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Husain, Aban Zehra. "Verma Modules, The Weyl Character Formula and Embedding Theorems." Thesis, Uppsala universitet, Algebra och geometri, 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-386041.

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19

Najid, Abdelouahhab. "Série de Poincaré des modules gradués génériques." Grenoble 1, 1986. http://www.theses.fr/1986GRE10107.

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R designant l'anneau des polynomes a n indeterminees sur un corps, gradue de facon naturelle, m est un r-module gradue generique et f::(0)(m) son 0-ieme ideal de fitting. Utilisant les resolutions libres graduees de m et r/f::(0)(m) fournies par buchsbaum-eisenbud et eagon-northcott, on montre que si dim supp m = d, les series de poincare p(u) de m et q(u) de r/f::(0)(m) sont des fractions rationnelles ayant un pole d'ordre d exactement en u = 1 avec pour coefficient e::(s-t+1) -e::(s-t)h::(1) +. . . +(-1)**(s-t+1)h::(s-t+1) ou m est defini par la presentation graduee r(lambda ::(1)) cercle+. . . Cercle+ r(lambda ::(s)) -> r(epsilon ::(1)) cercle+. . . Cercle+ r(epsilon ::(t)) -> m -> 0 avec s superieur ou egal a t, lambda ::(1),. . . ,lambda ::(s), epsilon ::(1),. . . , epsilon ::(t) etant des entiers positifs ou nuls. Ici e::(i) designe la i-eme fonction symetrique elementaire en lambda ::(1),. . . ,lambda ::(s) et h::(i) la i-eme fonction symetrique complete en epsilon ::(1),. . . , epsilon ::(t). Si d = 0, ceci entraine que m et r/f::(0)(m) sont des k-espaces vectoriels de rang e::(n)-e::(n-1)h::(1)+. . . +(-1)**(n)h::(n). Si d = 1 et k est algebriquement clos, on donne une demonstration elementaire d'un theoreme du type "bezout" pour les modules generiques

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20

Segal, Joel. "Pointwise conjugate groups and modules over the Steenrod algebra." Doctoral thesis, [S.l. : s.n.], 1999. http://deposit.ddb.de/cgi-bin/dokserv?idn=963672304.

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21

Steinberg, David. "Homological Properties of Standard KLR Modules." Thesis, University of Oregon, 2017. http://hdl.handle.net/1794/22292.

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Khovanov-Lauda-Rouquier algebras, or KLR algebras, are a family of algebras known to categorify the upper half of the quantized enveloping algebra of a given Lie algebra. In finite type, these algebras come with a family of standard modules, which correspond to PBW bases under this categorification. In this thesis, we show that there are no non-zero homomorphisms between distinct standard modules and that all non-zero endomorphisms of standard modules are injective. We then apply this result to obtain applications to the modular representation theory of KLR algebras. Restricting our attention to finite type A, we are then able to compute explicit projective resolutions of all standard modules. Finally, in finite type A when alpha is a positive root, we let D be the direct sum of all distinct standard modules and compute the algebra structure on Ext(D, D). This dissertation includes unpublished co-authored material.

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22

Carstensen, Vivi. "On characteristic p Verma modules and subalgebras of the hyperalgebra." Thesis, University of Oxford, 1994. http://ora.ox.ac.uk/objects/uuid:c6f5db9a-db94-4d58-9eb1-dd402c8846c5.

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Let G be a finite dimensional semisimple Lie algebra; we study the class of infinite dimensional representations of Gcalled characteristic p Verma modules. To obtain information about the structure of the Verma module Z(λ) we find primitive weights μ such that a non-zero homomorphism from Z(μ) to Z(λ) exists. For λ + ρ dominant, where ρ is the sum of the fundamental roots, there exist only finitely many primitive weights, and they all appear in a convex, bounded area. In the case of λ + ρ not dominant, and the characteristic p a good prime, there exist infinitely many primitive weights for the Lie algebra. For G = sl₃ we explicitly present a large, but not necessarily complete, set of primitive weights. A method to obtain the Verma module as the tensor product of Steinberg modules and Frobenius twisted Z(λ₁) is given for certain weights, λ = pⁿ λ₁ + (pⁿ — 1)ρ. Furthermore, a result about exact sequences of Weyl modules is carried over to Verma modules for sl₂. Finally, the connection between the subalgebra u¯₁ of the hyperalgebra U for a finite dimensional semisimple Lie algebra, and a group algebra KG for some suitable p-group G is studied. No isomorphism exists, when the characteristic of the field is larger than the Coxeter number. However, in the case of p — 2 we find u¯₁sl₃≈ KG. Furthermore, we determine the centre ofu¯_nsl₃, and we obtain an alternative K-basis of U-.

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Çetindil, Yasin Alizade Rafail. "Generalization of cofinitely supplemented modules to lattıces /." [S.l. : s.n.], 2005. http://library.iyte.edu.tr/tezler/master/matematik/T000402.pdf.

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Thesis (Master)--İzmir Institute of Technology, İzmir, 2005.
Keywords: Supplemented modules, cofinitely supplemented modules, cofinitely supplemented lattices, generalization of supplemented modules, generalization of cofinitely supplemented modules. Includes bibliographical references (leaves .p26).

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Corlett, Kelvin. "On homomorphisms between Specht modules for the Ariki-Koike algebra." Thesis, University of East Anglia, 2012. https://ueaeprints.uea.ac.uk/47289/.

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Specht modules occupy a position of central importance in the representation theory of both the symmetric and Iwahori-Hecke algebras, and there is hence considerable interest in achieving a greater understanding of their structure. To this end, over the past thirty years there has been much study undertaken of the homomorphism spaces between these modules, with a particular emphasis being placed upon the construction of explicit homomorphisms between Specht modules. Being a generalization of the Iwahori-Hecke algebra of type A, Specht modules are of a similar importance to the Ariki-Koike algebra. In this thesis we provide and analogue of James’s kernel intersection theorem, the latter having been a key tool in the study of homomorphisms between Specht modules in the setting of both the symmetric group and the Iwahori-Hecke algebra of type A. We also provide and outline of how this result may be used to construct homomorphisms between Specht modules for the Iwahori-Hecke algebra of type B. Additionally, as a byproduct of this work, we include a sufficient condition for certain kinds of commonly encountered tableaux to determine homomorphisms between analogues of Young’s permutation modules and the Specht modules.

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Buckner, Joshua Dugas Manfred. "On rings with distinguished ideals and their modules." Waco, Tex. : Baylor University, 2007. http://hdl.handle.net/2104/5025.

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Drube, Paul Harlan. "TQFT diffeomorphism invariants and skein modules." Diss., University of Iowa, 2011. https://ir.uiowa.edu/etd/952.

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There is a well-known correspondence between two-dimensional topological quantum field theories (2-D TQFTs) and commutative Frobenius algebras. Every 2-D TQFT also gives rise to a diffeomorphism invariant of closed, orientable two-manifolds, which may be investigated via the associated commutative Frobenius algebras. We investigate which such diffeomorphism invariants may arise from TQFTs, and in the process uncover a distinction between two fundamentally different types of commutative Frobenius algebras ("weak" Frobenius algebras and "strong" Frobenius algebras). These diffeomorphism invariants form the starting point for our investigation into marked cobordism categories, which generalize the local cobordism relations developed by Dror Bar-Natan during his investigation of Khovanov's link homology. We subsequently examine the particular class of 2-D TQFTs known as "universal sl(n) TQFTs". These TQFTs are at the algebraic core of the link invariants known as sl(n) link homology theories, as they provide the algebraic structure underlying the boundary maps in those homology theories. We also examine the 3-manifold diffeomorphism invariants known as skein modules, which were first introduced by Marta Asaeda and Charles Frohman. These 3-manifold invariants adapt Bar-Natan's marked cobordism category (as induced by a specific 2-D TQFT) to embedded surfaces, and measure which such surfaces may be embedded within in 3-manifold (modulo Bar-Natan's local cobordism relations). Our final results help to characterize the structure of such skein modules induced by universal sl(n) TQFTs.

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Lescot, Jack. "Contribution à l'étude des series de Bass." Caen, 1985. http://www.theses.fr/1985CAEN2030.

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Soient r un anneau unitaire commutatif local noetherien de corps residuel k, et m un r-module de type fine. Contribution a l'etude de deux series formelles associees a m, la serie de poincare: p::(r)**(m)(t)=sigma ::(i >ou= o) dim::(k) tor::(i)**(r)(m, k)t**(i) et la serie de bass: i::(r)**(m)(t)=sigma ::(i >ou= o) dim::(k) ext::(r)**(i)(k, m)t**(i). Soit f:s->r un homomorphisme local surjectif. Etude de la famille des r-modules dont les series de poincare verifient p::(r)**(m)(t)/p::(r)**(k)(t)=p::(s)**(m)(t)/p::(s)**(k)(t). Obtention d'un theoreme de reduction au cas artenien pour les series de bass. Calcul des series de poincare et de bass de certains produits fibres d'anneaux. Etude d'un produit homologique associe a m. Obtention de relations entre la serie de bass de m et celles de ces modules de syzygie. Obtention de formules de changement d'anneaux par certains homomorphismes de golod pour les series de bass. Etude du comportement asymptotique des dim::(k) tor::(i)**(r)(m, k) sur certains anneaux

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Toft, Tea. "Auslander-Reiten components containing modules of finite complexity." Thesis, Norges teknisk-naturvitenskapelige universitet, Institutt for matematiske fag, 2011. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-12937.

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Let R be a connected selfinjective Artin algebra. We prove that any almost split sequence ending at an Omega-perfect R-module of finite complexity has at most four non-projective summands in a chosen decomposition of the middle term into indecomposable modules. Moreover, we show that a chosen decomposition into indecomposable modules of the middle term of an almost split sequence ending at an R-module of complexity 1 lying in a regular component of the Auslander-Reiten quiver has at most two summands. Furthermore, we prove that the regular component is of type ZA_{infinity} or ZA_{infinity}/. We use this to study modules with eventually constant and eventually periodic Betti numbers.

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29

Zander, Shirley Jo Friedberg Stephen H. "Applied mathematical modules for use in a linear algebra service course." Normal, Ill. Illinois State University, 1990. http://wwwlib.umi.com/cr/ilstu/fullcit?p9101130.

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Thesis (D.A.)--Illinois State University, 1990.
Title from title page screen, viewed November 16, 2005. Dissertation Committee: Stephen Friedberg (chair), John Dossey, George Kidder, Michael Plantholt, Robert Ritt. Includes bibliographical references (leaves 22-23) and abstract. Also available in print.

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30

Ma, Biao [Verfasser]. "Faithfully Balanced Modules and Applications in Relative Homological Algebra / Biao Ma." Bielefeld : Universitätsbibliothek Bielefeld, 2019. http://d-nb.info/1196644071/34.

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31

Kahn, Constantin P. M. "Reflexive Moduln auf einfach-elliptischen Flächensingularitäten." Bonn : [s.n.], 1988. http://catalog.hathitrust.org/api/volumes/oclc/18440118.html.

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32

Wackwitz, Daniel Joseph. "Versal deformation rings of modules over Brauer tree algebras." Diss., University of Iowa, 2015. https://ir.uiowa.edu/etd/1926.

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This thesis applies methods from the representation theory of finite dimensional algebras, specifically Brauer tree algebras, to the study of versal deformation rings of modules for these algebras. The main motivation for studying Brauer tree algebras is that they generalize p-modular blocks of group rings with cyclic defect groups. We consider the case when Λ is a Brauer tree algebra over an algebraically closed field K and determine the structure of the versal deformation ring R(Λ,V) of every indecomposable Λ-module V when the Brauer tree is a star whose exceptional vertex is at the center. The ring R(Λ,V) is a complete local commutative Noetherian K-algebra with residue field K, which can be expressed as a quotient ring of a power series algebra over K in finitely many commuting variables. The defining property of R(Λ,V) is that the isomorphism class of every lift of V over a complete local commutative Noetherian K-algebra R with residue field K arises from a local ring homomorphism α : R(Λ, V )→R and that α is unique if R is the ring of dual numbers k[t]/(t2). In the case where Λ is a star Brauer tree algebra and V is an indecomposable Λ-module such that the K-dimension of Ext1Λ(V,V) is equal to R, we explicitly determine generators of an ideal J of k[[t1,....,tr]] such that R(Λ,V)≅k[[t1,....,tr]]/J.

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Bagnoli, Lucia <1993&gt. "Finite irreducible modules over the conformal superalgebras K'_4 and CK_6." Doctoral thesis, Alma Mater Studiorum - Università di Bologna, 2021. http://amsdottorato.unibo.it/9744/1/bagnoli_lucia_tesi.pdf.

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In this thesis we classify all finite irreducible modules over the conformal superalgebra K'_4 by means of their correspondence with irreducible finite conformal modules over the annihilation superalgebra associated with K'_4. We obtain that degenerate Verma modules over the annihilation superalgebra associated with K'_4 are part of infinite complexes and the number of these complexes is infinite; we compute the homology of these complexes with techniques of spectral sequences and provide an explicit realization of all irreducible quotients. We prove a technical result, stated by Boyallian, Kac and Liberati, on singular vectors of degenerate Verma modules over the annihilation superalgebra associated with CK_6. We start the computation of the homology of the diagram of infinite complexes of degenerate Verma modules for CK_6 found by Boyallian, Kac and Liberati.

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Frisk, Dubsky Brendan. "Classication of simple complex weight modules with finite-dimensional weight spaces over the Schrödinger algebra." Thesis, Uppsala universitet, Algebra och geometri, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-200606.

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YU, HONGMIAO. "Liaison by Quasi-Gorenstein Ideals and N-fiber-full Modules." Doctoral thesis, Università degli studi di Genova, 2022. http://hdl.handle.net/11567/1093933.

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Minardi, John. "Iwasawa modules for [p-adic]-extensions of algebraic number fields /." Thesis, Connect to this title online; UW restricted, 1986. http://hdl.handle.net/1773/5742.

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Salminen, Adam D. "On the sources of simple modules in nilpotent blocks." Connect to resource, 2005. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1124221435.

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Thesis (Ph. D.)--Ohio State University, 2005.
Title from first page of PDF file. Document formatted into pages; contains viii, 87 p. Includes bibliographical references (p. 85-87). Available online via OhioLINK's ETD Center

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Kong, Maynard. "Characteristic classes of modules." Pontificia Universidad Católica del Perú, 2014. http://repositorio.pucp.edu.pe/index/handle/123456789/97347.

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In this paper we have developed a general theory of characteristic classes of modules. To a given invariant map defined on a Lie algebra, we associate a cohomology class by using the curvature form of a certain kind of connections. Here we present a very simple proof of the invariance theorem (Theorem 12), which states that equivalent connections give rise to the same characteristic class. We have used those invariant maps of {9} to define Chern classes of projective modules and we have derived their basic properties. It might be interesting to observe that this theory could be applied to define characteristic classes of bilinear maps. In particular, the Euler classes of {6} can be obtained in this way.

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39

Prince, R. N. "On the theory of Krull rings and injective modules." Master's thesis, University of Cape Town, 1988. http://hdl.handle.net/11427/22179.

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In the first chapter we give an outline of classical KRULL rings as in SAMUEL (1964), BOURBAKI (1965) and FOSSUM (1973). In the second chapter we introduce two notions important to our treatment of KRULL theory. The first is injective modules and.the second torsion theories. We then look at injective modules over Noetherian rings as in MATLIS [1958] and then over KRULL rings as in BECK [1971]. We show that for a KRULL ring there is a torsion theory (N,M) where N is the pseudo-zero modules and M the set of N-torsion-free (BECK calls these co-divisorial) modules. From LAMBEK [1971] there is a full abelian sub category C, namely the category of N-torsion-free, N-divisible modules, with exact reflector. We show in C (I) every direct sum of injective modules is injective and (II) C has global dimension at most one. It is these two properties that we exploit in the third chapter to give another characterization of KRULL rings. Then we generalize this to rings with zero-divisors and find that (i) R has to be reduced (ii) the ring is KRULL if and only if it is a finite product of fields and KRULL domains (iii) the injective envelope of the ring is semi-simple artinian. We then generalize the ideas to rings of higher dimension.

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40

PAVIA, EMANUELE. "MIXED GRADED MODULES IN HOMOTOPY LIE THEORY." Doctoral thesis, Università degli Studi di Milano, 2022. http://hdl.handle.net/2434/930979.

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L’obiettivo principale di questa tesi è lo studio dei complessi misti graduati e del loro possibile ruolo nell’ambito della ricerca nella teoria della deformazione. In particolare, mi sono occupato della relazione tra complessi misti graduati e algebre di Lie derivate. I due contributi principali di questa tesi sono la costruzione di una t-struttura completa e non-degenere sulla ∞-categoria stabile dei complessi misti graduati, che esibisce i moduli misti graduati come il completamento sinistro della t-struttura di Beilinson sulla ∞-categoria derivata filtrata, e la costruzione di una famiglia di funtori di Chevalley-Eilenberg verso la ∞-categoria dei moduli misti graduati. Nonostante sia noto che i complessi di Chevalley-Eilenberg siano dotati di questa struttura, in letteratura tale funtore non è mai stato costruito in maniera indipendente da qualsiasi modello per le ∞-categorie.
The main objective of this thesis is to study mixed graded complexes as a framework where to study derived deformation theory. In particular, I investigated the relationship between mixed graded complexes and derived Lie algebras. The main contributions of this thesis are the following. First, I provided the ∞-category of mixed graded complexes with a complete and non-degenerate t-structure, which exhibits such ∞-category as the left completion of the Beilinson t-structure on the filtered derived ∞-category. Secondly, I constructed a family of Chevalley-Eilenberg ∞-functors computing homology and cohomology of derived Lie algebras, endowing them of a richer structure of mixed graded complexes. Even if it is known that Chevalley-Eilenberg complexes are endowed with such structure, my construction is new and completely model-independent.

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Brown, Wesley R. Goeters Herman Pat. "Torsionless modules and minimal generating sets for ideals of integral domains." Auburn, Ala., 2006. http://repo.lib.auburn.edu/2006%20Summer/Theses/BROWN_WESLEY_55.pdf.

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Wakefield, Max. "On the derivation module and apolar algebra of an arrangement of hyperplanes /." view abstract or download file of text, 2006. http://proquest.umi.com/pqdweb?did=1188874511&sid=1&Fmt=2&clientId=11238&RQT=309&VName=PQD.

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Thesis (Ph. D.)--University of Oregon, 2006.
Typescript. Includes vita and abstract. Includes bibliographical references (leaves 83-84). Also available for download via the World Wide Web; free to University of Oregon users.

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43

Randrianarisoa, Tovohery Hajatiana. "Drinfeld modules and their application to factor polynomials." Thesis, Stellenbosch : Stellenbosch University, 2012. http://hdl.handle.net/10019.1/71872.

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Thesis (MSc)--Stellenbosch University, 2012.
ENGLISH ABSTRACT: Major works done in Function Field Arithmetic show a strong analogy between the ring of integers Z and the ring of polynomials over a nite eld Fq[T]. While an algorithm has been discovered to factor integers using elliptic curves, the discovery of Drinfeld modules, which are analogous to elliptic curves, made it possible to exhibit an algorithm for factorising polynomials in the ring Fq[T]. In this thesis, we introduce the notion of Drinfeld modules, then we demonstrate the analogy between Drinfeld modules and Elliptic curves. Finally, we present an algorithm for factoring polynomials over a nite eld using Drinfeld modules.
AFRIKAANSE OPSOMMING: 'n Groot deel van die werk wat reeds in funksieliggaam rekenkunde voltooi is toon 'n sterk verband tussen die ring van heelgetalle, Z; en die ring van polinome oor 'n eindige liggaam, F[T]: Terwyl daar alreeds 'n algoritme, wat gebruik maak van elliptiese kurwes, ontwerp is om heelgetalle te faktoriseer, het die ontdekking van Drinfeld modules, wat analoog is aan elliptiese kurwes, dit moontlik gemaak om 'n algoritme te konstrueer om polinome in die ring F[T] te faktoriseer. In hierdie tesis maak ons die konsep van Drinfeld modules bekend deur sekere aspekte daarvan te bestudeer. Ons gaan voort deur 'n voorbeeld te voorsien wat die analoog tussen Drinfeld modules en elliptiese kurwes illustreer. Uiteindelik, deur gebruik te maak van Drinfeld modules, bevestig ons hierdie analoog deur die algoritme vir die faktorisering van polinome oor eindige liggame te veskaf.

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Guo, Xiuzhan. "Monadicity, purity and descent equivalence /." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2000. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp02/NQ59136.pdf.

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Vyas, Rishi. "Ore localization and the Ischebeck spectral sequence." Thesis, University of Cambridge, 2013. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.607967.

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Drinen, Michael Jeffrey. "Iwasawa mu-invariants of Selmer groups /." Thesis, Connect to this title online; UW restricted, 1999. http://hdl.handle.net/1773/5810.

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47

Fusacchia, Gabriele. "Injective modules over semistar Noetherian domains." Doctoral thesis, Università degli studi di Padova, 2011. http://hdl.handle.net/11577/3427410.

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We approach the problem of classifying injective modules over an integral domain by using the tool of semistar operations. In light of the classical results obtained by Matlis in the case of Noetherian rings, we first study the structure of the so called semistar Noetherian domains, then we discuss how every semistar operation over a semistar Noetherian domain determines a special subclass of the injective modules which can be successfully classified in terms of cardinal invariants.
Questo lavoro affronta il problema della classificazione dei moduli iniettivi su di un dominio integro, usando lo strumento delle operazioni semistar. Prendendo spunto dai risultati classici di Matlis per il caso Noetheriano, viene prima studiata la struttura dei cosiddetti domini semistar Noetheriani, quindi viene mostrato come ogni operazione semistar su un tale dominio determini una sottoclasse speciale dei moduli iniettivi che può essere classificata in termini di invarianti cardinali.

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48

Kuwabara, Toshiro. "Characteristic cycles of standard modules for the rational Cherednik algebra of type Z/ιZ." 京都大学 (Kyoto University), 2008. http://hdl.handle.net/2433/136855.

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49

Brandt, Marco. "On unipotent Specht modules of finite general linear groups." [S.l. : s.n.], 2004. http://www.bsz-bw.de/cgi-bin/xvms.cgi?SWB11103979.

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Stavis, Andreas. "Representations of finite groups." Thesis, Karlstads universitet, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:kau:diva-69642.

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Representation theory is concerned with the ways of writing elements of abstract algebraic structures as linear transformations of vector spaces. Typical structures amenable to representation theory are groups, associative algebras and Lie algebras. In this thesis we study linear representations of finite groups. The study focuses on character theory and how character theory can be used to extract information from a group. Prior to that, concepts needed to treat character theory, and some of their ramifications, are investigated. The study is based on existing literature, with excessive use of examples to illuminate important aspects. An example treating a class of p-groups is also discussed.

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Dissertations / Theses on the topic 'Modules (Algebra)'

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