Modules over Non-Noetherian Domains
Modules over Non-Noetherian Domains

Author: László Fuchs

Publisher: American Mathematical Soc.

Published: 2001

Total Pages: 633

ISBN-13: 0821819631

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In this book, the authors present both traditional and modern discoveries in the subject area, concentrating on advanced aspects of the topic. Existing material is studied in detail, including finitely generated modules, projective and injective modules, and the theory of torsion and torsion-free modules. Some topics are treated from a new point of view. Also included are areas not found in current texts, for example, pure-injectivity, divisible modules, uniserial modules, etc. Special emphasis is given to results that are valid over arbitrary domains. The authors concentrate on modules over valuation and Prüfer domains, but also discuss Krull and Matlis domains, h-local, reflexive, and coherent domains. The volume can serve as a standard reference book for specialists working in the area and also is a suitable text for advanced-graduate algebra courses and seminars.

Commutative Algebra
Commutative Algebra

Author: Marco Fontana

Publisher: Springer Science & Business Media

Published: 2010-09-29

Total Pages: 491

ISBN-13: 144196990X

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Commutative algebra is a rapidly growing subject that is developing in many different directions. This volume presents several of the most recent results from various areas related to both Noetherian and non-Noetherian commutative algebra. This volume contains a collection of invited survey articles by some of the leading experts in the field. The authors of these chapters have been carefully selected for their important contributions to an area of commutative-algebraic research. Some topics presented in the volume include: generalizations of cyclic modules, zero divisor graphs, class semigroups, forcing algebras, syzygy bundles, tight closure, Gorenstein dimensions, tensor products of algebras over fields, as well as many others. This book is intended for researchers and graduate students interested in studying the many topics related to commutative algebra.

Rings, Modules, and Closure Operations
Rings, Modules, and Closure Operations

Author: Jesse Elliott

Publisher: Springer Nature

Published: 2019-11-30

Total Pages: 490

ISBN-13: 3030244016

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This book presents a systematic exposition of the various applications of closure operations in commutative and noncommutative algebra. In addition to further advancing multiplicative ideal theory, the book opens doors to the various uses of closure operations in the study of rings and modules, with emphasis on commutative rings and ideals. Several examples, counterexamples, and exercises further enrich the discussion and lend additional flexibility to the way in which the book is used, i.e., monograph or textbook for advanced topics courses.

Modules Over Discrete Valuation Domains
Modules Over Discrete Valuation Domains

Author: Piotr A. Krylov

Publisher: Walter de Gruyter

Published: 2008

Total Pages: 376

ISBN-13: 9783110200539

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"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.

Models, Modules and Abelian Groups
Models, Modules and Abelian Groups

Author: Rüdiger Göbel

Publisher: Walter de Gruyter

Published: 2008-12-10

Total Pages: 509

ISBN-13: 3110203030

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This is a memorial volume dedicated to A. L. S. Corner, previously Professor in Oxford, who published important results on algebra, especially on the connections of modules with endomorphism algebras. The volume contains refereed contributions which are related to the work of Corner. It contains also an unpublished extended paper of Corner himself. A memorial volume with important contributions related to algebra.

Integral Closure of Ideals, Rings, and Modules
Integral Closure of Ideals, Rings, and Modules

Author: Craig Huneke

Publisher: Cambridge University Press

Published: 2006-10-12

Total Pages: 446

ISBN-13: 0521688604

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Ideal for graduate students and researchers, this book presents a unified treatment of the central notions of integral closure.

An Introduction to Noncommutative Noetherian Rings
An Introduction to Noncommutative Noetherian Rings

Author: K. R. Goodearl

Publisher: Cambridge University Press

Published: 2004-07-12

Total Pages: 372

ISBN-13: 9780521545372

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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.

Abelian Groups, Rings, Modules, and Homological Algebra
Abelian Groups, Rings, Modules, and Homological Algebra

Author: Pat Goeters

Publisher: CRC Press

Published: 2016-04-19

Total Pages: 354

ISBN-13: 142001076X

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About the book In honor of Edgar Enochs and his venerable contributions to a broad range of topics in Algebra, top researchers from around the world gathered at Auburn University to report on their latest work and exchange ideas on some of today's foremost research topics. This carefully edited volume presents the refereed papers of the par

Integral Domains Inside Noetherian Power Series Rings: Constructions and Examples
Integral Domains Inside Noetherian Power Series Rings: Constructions and Examples

Author: William Heinzer

Publisher: American Mathematical Soc.

Published: 2021-10-08

Total Pages: 426

ISBN-13: 1470466422

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Power series provide a technique for constructing examples of commutative rings. In this book, the authors describe this technique and use it to analyse properties of commutative rings and their spectra. This book presents results obtained using this approach. The authors put these results in perspective; often the proofs of properties of classical examples are simplified. The book will serve as a helpful resource for researchers working in commutative algebra.

Non-Noetherian Commutative Ring Theory
Non-Noetherian Commutative Ring Theory

Author: S.T. Chapman

Publisher: Springer Science & Business Media

Published: 2000-10-31

Total Pages: 504

ISBN-13: 9780792364924

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This volume consists of twenty-one articles by many of the most prominent researchers in non-Noetherian commutative ring theory. The articles combine in various degrees surveys of past results, recent results that have never before seen print, open problems, and an extensive bibliography. One hundred open problems supplied by the authors have been collected in the volume's concluding chapter. The entire collection provides a comprehensive survey of the development of the field over the last ten years and points to future directions of research in the area. Audience: Researchers and graduate students; the volume is an appropriate source of material for several semester-long graduate-level seminars and courses.