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Laurent Series Rings And Related Rings

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Laurent Series Rings And Related Rings

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Author : Askar Tuganbaev
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2020-09-21

Laurent Series Rings And Related Rings written by Askar Tuganbaev and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-21 with Mathematics categories.

In this book, ring-theoretical properties of skew Laurent series rings A((x; φ)) over a ring A, where A is an associative ring with non-zero identity element are described. In addition, we consider Laurent rings and Malcev-Neumann rings, which are proper extensions of skew Laurent series rings.

Laurent Series Rings And Related Rings

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Author : Askar Tuganbaev
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2020-09-21

Semidistributive Modules And Rings

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Author : A.A. Tuganbaev
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Semidistributive Modules And Rings written by A.A. Tuganbaev and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

A module M is called distributive if the lattice Lat(M) of all its submodules is distributive, i.e., Fn(G + H) = FnG + FnH for all submodules F,G, and H of the module M. A module M is called uniserial if all its submodules are comparable with respect to inclusion, i.e., the lattice Lat(M) is a chain. Any direct sum of distributive (resp. uniserial) modules is called a semidistributive (resp. serial) module. The class of distributive (resp. semidistributive) modules properly cont.ains the class ofall uniserial (resp. serial) modules. In particular, all simple (resp. semisimple) modules are distributive (resp. semidistributive). All strongly regular rings (for example, all factor rings of direct products of division rings and all commutative regular rings) are distributive; all valuation rings in division rings and all commutative Dedekind rings (e.g., rings of integral algebraic numbers or commutative principal ideal rings) are distributive. A module is called a Bezout module or a locally cyclic module ifevery finitely generated submodule is cyclic. If all maximal right ideals of a ring A are ideals (e.g., if A is commutative), then all Bezout A-modules are distributive.

Modules Over Discrete Valuation Domains

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Author : Piotr A. Krylov
language : en
Publisher: Walter de Gruyter
Release Date : 2008

Modules Over Discrete Valuation Domains written by Piotr A. Krylov and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.

"In this book, modules over a specific class of rings, the discrete valuations domains, are considered. Such modules call for a special consideration, since they have specific properties and play an important role in various areas of algebra, especially of commutative algebra. The text is accompanied by exercises, historical remarks, links to related fields and open problems. It is useful for students, graduates studying algebra, young researchers, and experts."--BOOK JACKET.

Rings Close To Regular

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Author : A.A. Tuganbaev
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09

Rings Close To Regular written by A.A. Tuganbaev and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.

Preface All rings are assumed to be associative and (except for nilrings and some stipulated cases) to have nonzero identity elements. A ring A is said to be regular if for every element a E A, there exists an element b E A with a = aba. Regular rings are well studied. For example, [163] and [350] are devoted to regular rings. A ring A is said to be tr-regular if for every element a E A, there is an element n b E A such that an = anba for some positive integer n. A ring A is said to be strongly tr-regular if for every a E A, there is a positive integer n with n 1 n an E a + An Aa +1. It is proved in [128] that A is a strongly tr-regular ring if and only if for every element a E A, there is a positive integer m with m 1 am E a + A. Every strongly tr-regular ring is tr-regular [38]. If F is a division ring and M is a right vector F-space with infinite basis {ei}~l' then End(MF) is a regular (and tr-regular) ring that is not strongly tr-regular. The factor ring of the ring of integers with respect to the ideal generated by the integer 4 is a strongly tr-regular ring that is not regular.

Modules Over Discrete Valuation Rings

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Author : Piotr A. Krylov
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2018-09-24

Modules Over Discrete Valuation Rings written by Piotr A. Krylov and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-09-24 with Mathematics categories.

This book provides the first systematic treatment of modules over discrete valuation domains, which play an important role in various areas of algebra, especially in commutative algebra. Many important results representing the state of the art are presented in the text along with interesting open problems. This updated edition presents new approaches on p-adic integers and modules, and on the determinability of a module by its automorphism group. ContentsPreliminariesBasic factsEndomorphism rings of divisible and complete modulesRepresentation of rings by endomorphism ringsTorsion-free modulesMixed modulesDeterminity of modules by their endomorphism ringsModules with many endomorphisms or automorphisms

An Introduction To Noncommutative Noetherian Rings

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Author : K. R. Goodearl
language : en
Publisher: Cambridge University Press
Release Date : 2004-07-12

An Introduction To Noncommutative Noetherian Rings written by K. R. Goodearl and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-07-12 with Mathematics categories.

This introduction to noncommutative noetherian rings is intended to be accessible to anyone with a basic background in abstract algebra. It can be used as a second-year graduate text, or as a self-contained reference. Extensive explanatory discussion is given, and exercises are integrated throughout. This edition incorporates substantial revisions, particularly in the first third of the book, where the presentation has been changed to increase accessibility and topicality. New material includes the basic types of quantum groups, which then serve as test cases for the theory developed.

A First Course In Noncommutative Rings

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Author : Tsit-Yuen Lam
language : en
Publisher: Springer Science & Business Media
Release Date : 2001-06-21

A First Course In Noncommutative Rings written by Tsit-Yuen Lam and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-06-21 with Mathematics categories.

Aimed at the novice rather than the connoisseur and stressing the role of examples and motivation, this text is suitable not only for use in a graduate course, but also for self-study in the subject by interested graduate students. More than 400 exercises testing the understanding of the general theory in the text are included in this new edition.

Ring Constructions And Applications

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Author : Andrei V. Kelarev
language : en
Publisher: World Scientific
Release Date : 2002

Ring Constructions And Applications written by Andrei V. Kelarev and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.

This book contains the definitions of several ring constructions used in various applications. The concept of a groupoid-graded ring includes many of these constructions as special cases and makes it possible to unify the exposition. Recent research results on groupoid-graded rings and more specialized constructions are presented. In addition, there is a chapter containing open problems currently considered in the literature. Ring Constructions and Applications can serve as an excellent introduction for graduate students to many ring constructions as well as to essential basic concepts of group, semigroup and ring theories used in proofs.

Introduction To Ring Theory

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Author : Paul M. Cohn
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Introduction To Ring Theory written by Paul M. Cohn and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

A clear and structured introduction to the subject. After a chapter on the definition of rings and modules there are brief accounts of Artinian rings, commutative Noetherian rings and ring constructions, such as the direct product, Tensor product and rings of fractions, followed by a description of free rings. Readers are assumed to have a basic understanding of set theory, group theory and vector spaces. Over two hundred carefully selected exercises are included, most with outline solutions.

Laurent Series Rings And Related Rings

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