Modules Over Non Noetherian Domains
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| Author | : László Fuchs |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 633 |
| Release | : 2001 |
| Genre | : Mathematics |
| ISBN | : 0821819631 |
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.
| Author | : Marco Fontana |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 491 |
| Release | : 2010-09-29 |
| Genre | : Mathematics |
| ISBN | : 144196990X |
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.
| Author | : Craig Huneke |
| Publisher | : Cambridge University Press |
| Total Pages | : 446 |
| Release | : 2006-10-12 |
| Genre | : Mathematics |
| ISBN | : 0521688604 |
Ideal for graduate students and researchers, this book presents a unified treatment of the central notions of integral closure.
| Author | : K. R. Goodearl |
| Publisher | : Cambridge University Press |
| Total Pages | : 372 |
| Release | : 2004-07-12 |
| Genre | : Mathematics |
| ISBN | : 9780521545372 |
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.
| Author | : Jesse Elliott |
| Publisher | : Springer Nature |
| Total Pages | : 490 |
| Release | : 2019-11-30 |
| Genre | : Mathematics |
| ISBN | : 3030244016 |
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.
| Author | : William Heinzer |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 426 |
| Release | : 2021-10-08 |
| Genre | : Education |
| ISBN | : 1470466422 |
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.
| Author | : Piotr A. Krylov |
| Publisher | : Walter de Gruyter |
| Total Pages | : 376 |
| Release | : 2008 |
| Genre | : Mathematics |
| ISBN | : 9783110200539 |
"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.
| Author | : Rüdiger Göbel |
| Publisher | : Walter de Gruyter |
| Total Pages | : 509 |
| Release | : 2008-12-10 |
| Genre | : Mathematics |
| ISBN | : 3110203030 |
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.
| Author | : Pat Goeters |
| Publisher | : CRC Press |
| Total Pages | : 354 |
| Release | : 2016-04-19 |
| Genre | : Mathematics |
| ISBN | : 142001076X |
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
| Author | : Piotr A. Krylov |
| Publisher | : Walter de Gruyter GmbH & Co KG |
| Total Pages | : 397 |
| Release | : 2018-09-24 |
| Genre | : Mathematics |
| ISBN | : 3110609851 |
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. Contents Preliminaries Basic facts Endomorphism rings of divisible and complete modules Representation of rings by endomorphism rings Torsion-free modules Mixed modules Determinity of modules by their endomorphism rings Modules with many endomorphisms or automorphisms
