Artinian Modules over Group Rings

Artinian Modules over Group Rings
Author: Leonid Kurdachenko
Publisher: Springer Science & Business Media
Total Pages: 253
Release: 2006-12-22
Genre: Mathematics
ISBN: 3764377658

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This book highlights important developments on artinian modules over group rings of generalized nilpotent groups. Along with traditional topics such as direct decompositions of artinian modules, criteria of complementability for some important modules, and criteria of semisimplicity of artinian modules, it also focuses on recent advanced results on these matters.

Groups, Rings, Modules

Groups, Rings, Modules
Author: Maurice Auslander
Publisher: Courier Corporation
Total Pages: 484
Release: 2014-06-01
Genre: Mathematics
ISBN: 048679542X

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Classic monograph covers sets and maps, monoids and groups, unique factorization domains, localization and tensor products, applications of fundamental theorem, algebraic field extension, Dedekind domains, and much more. 1974 edition.

Noetherian Rings and Their Applications

Noetherian Rings and Their Applications
Author: Lance W. Small
Publisher: American Mathematical Soc.
Total Pages: 130
Release: 1987
Genre: Mathematics
ISBN: 0821815253

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". T. Stafford -- The Goldie rank of a module " . R. Farkas -- Noetherian group rings: An exercise in creating folklore and intuition " . C. Jantzen -- Primitive ideals in the enveloping algebra of a semisimple Lie algebra " . J. Enright -- Representation theory of semisimple Lie algebras " .-E. Björk -- Filtered Noetherian rings " . Rentschler -- Primitive ideals in enveloping algebras.

Infinite Groups

Infinite Groups
Author: Martyn R. Dixon
Publisher: CRC Press
Total Pages: 411
Release: 2022-12-30
Genre: Mathematics
ISBN: 1000848310

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In recent times, group theory has found wider applications in various fields of algebra and mathematics in general. But in order to apply this or that result, you need to know about it, and such results are often diffuse and difficult to locate, necessitating that readers construct an extended search through multiple monographs, articles, and papers. Such readers must wade through the morass of concepts and auxiliary statements that are needed to understand the desired results, while it is initially unclear which of them are really needed and which ones can be dispensed with. A further difficulty that one may encounter might be concerned with the form or language in which a given result is presented. For example, if someone knows the basics of group theory, but does not know the theory of representations, and a group theoretical result is formulated in the language of representation theory, then that person is faced with the problem of translating this result into the language with which they are familiar, etc. Infinite Groups: A Roadmap to Some Classical Areas seeks to overcome this challenge. The book covers a broad swath of the theory of infinite groups, without giving proofs, but with all the concepts and auxiliary results necessary for understanding such results. In other words, this book is an extended directory, or a guide, to some of the more established areas of infinite groups. Features An excellent resource for a subject formerly lacking an accessible and in-depth reference Suitable for graduate students, PhD students, and researchers working in group theory Introduces the reader to the most important methods, ideas, approaches, and constructions in infinite group theory.

Representations of Finite Groups

Representations of Finite Groups
Author: Hirosi Nagao
Publisher: Elsevier
Total Pages: 443
Release: 2014-05-10
Genre: Mathematics
ISBN: 1483269930

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Representations of Finite Groups provides an account of the fundamentals of ordinary and modular representations. This book discusses the fundamental theory of complex representations of finite groups. Organized into five chapters, this book begins with an overview of the basic facts about rings and modules. This text then provides the theory of algebras, including theories of simple algebras, Frobenius algebras, crossed products, and Schur indices with representation-theoretic versions of them. Other chapters include a survey of the fundamental theory of modular representations, with emphasis on Brauer characters. This book discusses as well the module-theoretic representation theory due to Green and includes some topics such as Burry–Carlson's theorem and Scott modules. The final chapter deals with the fundamental results of Brauer on blocks and Fong's theory of covering, and includes some approaches to them. This book is a valuable resource for readers who are interested in the various approaches to the study of the representations of groups.

Modules over the Integral Group Ring of a Non-Abelian Group of Order $pq$

Modules over the Integral Group Ring of a Non-Abelian Group of Order $pq$
Author: Lee Klingler
Publisher: American Mathematical Soc.
Total Pages: 138
Release: 1986
Genre: Group rings
ISBN: 0821823434

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By using pullbacks, we obtain a description of finitely generated modules over the integral group ring of a non-abelian group of order [italic]pq. The description is detailed enough to obtain information about the behavior of the modules in direct sums. We make the description more precise by relating it to the locally free class group of the integral group ring.

Associative and Non-Associative Algebras and Applications

Associative and Non-Associative Algebras and Applications
Author: Mercedes Siles Molina
Publisher: Springer Nature
Total Pages: 338
Release: 2020-01-02
Genre: Mathematics
ISBN: 3030352560

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This book gathers together selected contributions presented at the 3rd Moroccan Andalusian Meeting on Algebras and their Applications, held in Chefchaouen, Morocco, April 12-14, 2018, and which reflects the mathematical collaboration between south European and north African countries, mainly France, Spain, Morocco, Tunisia and Senegal. The book is divided in three parts and features contributions from the following fields: algebraic and analytic methods in associative and non-associative structures; homological and categorical methods in algebra; and history of mathematics. Covering topics such as rings and algebras, representation theory, number theory, operator algebras, category theory, group theory and information theory, it opens up new avenues of study for graduate students and young researchers. The findings presented also appeal to anyone interested in the fields of algebra and mathematical analysis.

Groups, Rings And Modules With Applications

Groups, Rings And Modules With Applications
Author: M.R. Adhikari
Publisher: Universities Press
Total Pages: 336
Release: 2003
Genre: Commutative rings
ISBN: 9788173714290

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Groups, Rings, Modules

Groups, Rings, Modules
Author: Maurice Auslander
Publisher: Courier Corporation
Total Pages: 484
Release: 2014-06-18
Genre: Mathematics
ISBN: 0486490823

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This classic monograph is geared toward advanced undergraduates and graduate students. The treatment presupposes some familiarity with sets, groups, rings, and vector spaces. The four-part approach begins with examinations of sets and maps, monoids and groups, categories, and rings. The second part explores unique factorization domains, general module theory, semisimple rings and modules, and Artinian rings. Part three's topics include localization and tensor products, principal ideal domains, and applications of fundamental theorem. The fourth and final part covers algebraic field extensions and Dedekind domains. Exercises are provided at the end of each chapter. Dover (2014) republication of the edition originally published by Harper & Row Publishers, New York, 1974. See every Dover book in print at www.doverpublications.com

Artinian Modules of Group Rings

Artinian Modules of Group Rings
Author: Leonid A. Kurdachenko
Publisher:
Total Pages: 247
Release: 2006
Genre:
ISBN: 9780817677640

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