Modules Over Discrete Valuation Rings

Author : Piotr A. Krylov,Askar A. Tuganbaev
Publisher : Walter de Gruyter GmbH & Co KG
Page : 337 pages
File Size : 54,9 Mb
Release : 2018-09-24
Category : Mathematics
ISBN : 9783110609851

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Modules over Discrete Valuation Rings by Piotr A. Krylov,Askar A. Tuganbaev Pdf

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

Author : Piotr A. Krylov,Askar A. Tuganbaev
Publisher : Walter de Gruyter
Page : 369 pages
File Size : 43,7 Mb
Release : 2008-08-27
Category : Mathematics
ISBN : 9783110205787

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Modules over Discrete Valuation Domains by Piotr A. Krylov,Askar A. Tuganbaev Pdf

This book provides the first systematic treatment of modules over discrete valuation domains which plays 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 which is supplemented by exercises and interesting open problems. An important contribution to commutative algebra.

Author : Piotr A. Krylov,Askar A. Tuganbaev
Publisher : Walter de Gruyter
Page : 376 pages
File Size : 42,5 Mb
Release : 2008
Category : Mathematics
ISBN : 3110200538

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Modules Over Discrete Valuation Domains by Piotr A. Krylov,Askar A. Tuganbaev Pdf

"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 : Piotr A. Krylov,Askar A. Tuganbaev
Publisher : Walter de Gruyter GmbH & Co KG
Page : 337 pages
File Size : 43,9 Mb
Release : 2018-09-24
Category : Mathematics
ISBN : 9783110611144

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Modules over Discrete Valuation Rings by Piotr A. Krylov,Askar A. Tuganbaev Pdf

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

Author : László Fuchs,Luigi Salce
Publisher : CRC Press
Page : 340 pages
File Size : 54,5 Mb
Release : 1985-03-27
Category : Mathematics
ISBN : 0824773268

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Modules over Valuation Rings by László Fuchs,Luigi Salce Pdf

This book initiates a systematic, in-depth study of Modules Over Valuation Domains. It introduces the theory of modules over commutative domains without finiteness conditions and examines frontiers of current research in modules over valuation domains. It represents a unique effort to combine ideas from abelian group theory, in a large scale, with powerful techniques developed in module theory. This volume surveys the background material on valuation rings, modules and homological algebra ... features new results for important classes of modules such as finitely generated, divisible, pure-injective, and projective dimension one -- never published before ... contains exercises and research problems -- offering guidance for independent and creative study ... and provides historical notes, comments, and an extensive bibliography. Mathematicians and advanced graduate-level mathematics students interested in module theory, abelian group theory, and commutative ring theory can stay abreast of the latest advances with Modules Over Valuation Domains. Book jacket.

Author : Irving Kaplansky
Publisher : Courier Dover Publications
Page : 112 pages
File Size : 41,6 Mb
Release : 2018-12-19
Category : Mathematics
ISBN : 9780486836454

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Infinite Abelian Groups by Irving Kaplansky Pdf

This concise monograph presents the theory of infinite abelian groups in a convenient form and helps students acquire some of the techniques used in modern infinite algebra. 1969 edition.

Author : Robin Hartshorne
Publisher : Springer Science & Business Media
Page : 520 pages
File Size : 40,8 Mb
Release : 1977-12-19
Category : Mathematics
ISBN : 0387902449

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Algebraic Geometry by Robin Hartshorne Pdf

This book provides an introduction to abstract algebraic geometry. It includes more than 400 exercises that offer specific examples as well as more specialized topics. From the reviews: "Enables the reader to make the drastic transition between the basic, intuitive questions about affine and projective varieties with which the subject begins, and the elaborate general methodology of schemes and cohomology employed currently to answer these questions." --MATHEMATICAL REVIEWS

Author : David F. Anderson,David Dobbs
Publisher : CRC Press
Page : 820 pages
File Size : 55,7 Mb
Release : 1995-04-10
Category : Mathematics
ISBN : 0824796055

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Zero-Dimensional Commutative Rings by David F. Anderson,David Dobbs Pdf

This work presents advances in zero-dimensional commutative rings and commutative algebra. It illustrates the research frontier with 52 open problems together with comments on the relevant literature, and offers a comprehensive index for easy access to information. Wide-ranging developments in commutative ring theory are examined.

Author : David Arnold
Publisher : Springer Science & Business Media
Page : 256 pages
File Size : 43,7 Mb
Release : 2012-11-14
Category : Mathematics
ISBN : 9781441987501

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Abelian Groups and Representations of Finite Partially Ordered Sets by David Arnold Pdf

The theme of this book is an exposition of connections between representations of finite partially ordered sets and abelian groups. Emphasis is placed throughout on classification, a description of the objects up to isomorphism, and computation of representation type, a measure of when classification is feasible. David M. Arnold is the Ralph and Jean Storm Professor of Mathematics at Baylor University. He is the author of "Finite Rank Torsion Free Abelian Groups and Rings" published in the Springer-Verlag Lecture Notes in Mathematics series, a co-editor for two volumes of conference proceedings, and the author of numerous articles in mathematical research journals.

Author : Craig Huneke,Irena Swanson
Publisher : Cambridge University Press
Page : 446 pages
File Size : 45,9 Mb
Release : 2006-10-12
Category : Mathematics
ISBN : 9780521688604

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Integral Closure of Ideals, Rings, and Modules by Craig Huneke,Irena Swanson Pdf

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

Author : Anonim
Publisher : Unknown
Page : 1026 pages
File Size : 44,6 Mb
Release : 1983-12
Category : Mathematics
ISBN : UCAL:B3981153

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Pacific Journal of Mathematics by Anonim Pdf

Author : Eben Matlis
Publisher : University of Chicago Press
Page : 180 pages
File Size : 40,7 Mb
Release : 1972
Category : Mathematics
ISBN : 0226510743

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Torsion-Free Modules by Eben Matlis Pdf

The subject of torsion-free modules over an arbitrary integral domain arises naturally as a generalization of torsion-free abelian groups. In this volume, Eben Matlis brings together his research on torsion-free modules that has appeared in a number of mathematical journals. Professor Matlis has reworked many of the proofs so that only an elementary knowledge of homological algebra and commutative ring theory is necessary for an understanding of the theory. The first eight chapters of the book are a general introduction to the theory of torsion-free modules. This part of the book is suitable for a self-contained basic course on the subject. More specialized problems of finding all integrally closed D-rings are examined in the last seven chapters, where material covered in the first eight chapters is applied. An integral domain is said to be a D-ring if every torsion-free module of finite rank decomposes into a direct sum of modules of rank 1. After much investigation, Professor Matlis found that an integrally closed domain is a D-ring if, and only if, it is the intersection of at most two maximal valuation rings.

Author : Anonim
Publisher : Unknown
Page : 974 pages
File Size : 41,8 Mb
Release : 1984
Category : Dissertations, Academic
ISBN : UOM:39015065651617

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Comprehensive Dissertation Index by Anonim Pdf

Vols. for 1973- include the following subject areas: Biological sciences, Agriculture, Chemistry, Environmental sciences, Health sciences, Engineering, Mathematics and statistics, Earth sciences, Physics, Education, Psychology, Sociology, Anthropology, History, Law & political science, Business & economics, Geography & regional planning, Language & literature, Fine arts, Library & information science, Mass communications, Music, Philosophy and Religion.

Author : Michael F. Atiyah,I.G. MacDonald
Publisher : CRC Press
Page : 140 pages
File Size : 43,5 Mb
Release : 2018-03-09
Category : Mathematics
ISBN : 9780429973260

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Introduction To Commutative Algebra by Michael F. Atiyah,I.G. MacDonald Pdf

First Published in 2018. This book grew out of a course of lectures given to third year undergraduates at Oxford University and it has the modest aim of producing a rapid introduction to the subject. It is designed to be read by students who have had a first elementary course in general algebra. On the other hand, it is not intended as a substitute for the more voluminous tracts such as Zariski-Samuel or Bourbaki. We have concentrated on certain central topics, and large areas, such as field theory, are not touched. In content we cover rather more ground than Northcott and our treatment is substantially different in that, following the modern trend, we put more emphasis on modules and localization.

Author : Anonim
Publisher : Unknown
Page : 828 pages
File Size : 40,7 Mb
Release : 2006
Category : Mathematics
ISBN : UOM:39015065183561

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Mathematical Reviews by Anonim Pdf