Approximations and Endomorphism Algebras of Modules

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Publisher : Walter de Gruyter
ISBN 13 : 3110218119
Total Pages : 1002 pages
Book Rating : 4.1/5 (12 download)

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Book Synopsis Approximations and Endomorphism Algebras of Modules by : Rüdiger Göbel

Download or read book Approximations and Endomorphism Algebras of Modules written by Rüdiger Göbel and published by Walter de Gruyter. This book was released on 2012-10-01 with total page 1002 pages. Available in PDF, EPUB and Kindle. Book excerpt: This second, revised and substantially extended edition of Approximations and Endomorphism Algebras of Modules reflects both the depth and the width of recent developments in the area since the first edition appeared in 2006. The new division of the monograph into two volumes roughly corresponds to its two central topics, approximation theory (Volume 1) and realization theorems for modules (Volume 2). It is a widely accepted fact that the category of all modules over a general associative ring is too complex to admit classification. Unless the ring is of finite representation type we must limit attempts at classification to some restricted subcategories of modules. The wild character of the category of all modules, or of one of its subcategories C, is often indicated by the presence of a realization theorem, that is, by the fact that any reasonable algebra is isomorphic to the endomorphism algebra of a module from C. This results in the existence of pathological direct sum decompositions, and these are generally viewed as obstacles to classification. In order to overcome this problem, the approximation theory of modules has been developed. The idea here is to select suitable subcategories C whose modules can be classified, and then to approximate arbitrary modules by those from C. These approximations are neither unique nor functorial in general, but there is a rich supply available appropriate to the requirements of various particular applications. The authors bring the two theories together. The first volume, Approximations, sets the scene in Part I by introducing the main classes of modules relevant here: the S-complete, pure-injective, Mittag-Leffler, and slender modules. Parts II and III of the first volume develop the key methods of approximation theory. Some of the recent applications to the structure of modules are also presented here, notably for tilting, cotilting, Baer, and Mittag-Leffler modules. In the second volume, Predictions, further basic instruments are introduced: the prediction principles, and their applications to proving realization theorems. Moreover, tools are developed there for answering problems motivated in algebraic topology. The authors concentrate on the impossibility of classification for modules over general rings. The wild character of many categories C of modules is documented here by the realization theorems that represent critical R-algebras over commutative rings R as endomorphism algebras of modules from C. The monograph starts from basic facts and gradually develops the theory towards its present frontiers. It is suitable both for graduate students interested in algebra and for experts in module and representation theory.

Approximations and Endomorphism Algebras of Modules

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Publisher : de Gruyter
ISBN 13 : 9783110110791
Total Pages : 0 pages
Book Rating : 4.1/5 (17 download)

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Book Synopsis Approximations and Endomorphism Algebras of Modules by : Rüdiger Göbel

Download or read book Approximations and Endomorphism Algebras of Modules written by Rüdiger Göbel and published by de Gruyter. This book was released on 2006 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The category of all modules over a general associative ring is too complex to admit any reasonable classification. Thus, unless the ring is of finite representation type, one must limit attempts at classification to some restricted subcategories of modules. The wild character of the category of all modules, or of one of its subcategories C is often indicated by the presence of a realization theorem, that is, by the fact that any reasonable algebra is isomorphic to the endomorphism algebra of a module from C. This results in the existence of pathological direct sum decompositions and these are generally viewed as obstacles to the classification. Realization theorems have thus become important indicators of the non-classification theory of modules. In order to overcome this problem, approximation theory of modules has been developed over the past few decades. The idea here is to select suitable subcategories C whose modules can be classified, and then to approximate arbitrary modules by ones from C. These approximations are neither unique nor functorial in general, but there is always a rich supply available appropriate to the requirements of various particular applications. Thus approximation theory has developed into an important part of the classification theory of modules. In this monograph the two methods are brought together. First the approximation theory of modules is developed and some of its recent applications, notably to infinite dimensional tilting theory, are presented. Then some prediction principles from set theory are introduced and these become the principal tools in the establishment of appropriate realization theorems. The monograph starts from basic facts and gradually develops the theory towards its present frontiers. It is suitable both for graduate students interested in algebra and for experts in module and representation theory.

Approximations and Endomorphism Algebras of Modules: Predictions

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Publisher : ISSN
ISBN 13 : 9783110218107
Total Pages : 0 pages
Book Rating : 4.2/5 (181 download)

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Book Synopsis Approximations and Endomorphism Algebras of Modules: Predictions by : Rüdiger Göbel

Download or read book Approximations and Endomorphism Algebras of Modules: Predictions written by Rüdiger Göbel and published by ISSN. This book was released on 2012 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph- now in its second revised and extended edition- provides a thorough treatment of module theory, a subfield of algebra. The authors develop an approximation theory as well as realization theorems and present some of its recent applications, notably to infinite-dimensional combinatorics and model theory. The book starts from basic facts and gradually develops the theory towards its present frontiers. It is suitable both for graduate students interested in algebra and for experts in module and representation theory.

Approximations and Endomorphism Algebras of Modules

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Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (816 download)

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Book Synopsis Approximations and Endomorphism Algebras of Modules by : Rüdiger Göbel

Download or read book Approximations and Endomorphism Algebras of Modules written by Rüdiger Göbel and published by . This book was released on 2012 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Arithmetical Rings and Endomorphisms

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Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110659824
Total Pages : 176 pages
Book Rating : 4.1/5 (16 download)

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Book Synopsis Arithmetical Rings and Endomorphisms by : Askar Tuganbaev

Download or read book Arithmetical Rings and Endomorphisms written by Askar Tuganbaev and published by Walter de Gruyter GmbH & Co KG. This book was released on 2019-06-04 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a comprehensive account of not necessarily commutative arithmetical rings, examining structural and homological properties of modules over arithmetical rings and summarising the interplay between arithmetical rings and other rings, whereas modules with extension properties of submodule endomorphisms are also studied in detail. Graduate students and researchers in ring and module theory will find this book particularly valuable.

Modules over Discrete Valuation Rings

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Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110609851
Total Pages : 397 pages
Book Rating : 4.1/5 (16 download)

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Book Synopsis Modules over Discrete Valuation Rings by : Piotr A. Krylov

Download or read book Modules over Discrete Valuation Rings written by Piotr A. Krylov and published by Walter de Gruyter GmbH & Co KG. This book was released on 2018-09-24 with total page 397 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Groups, Modules, and Model Theory - Surveys and Recent Developments

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Publisher : Springer
ISBN 13 : 331951718X
Total Pages : 493 pages
Book Rating : 4.3/5 (195 download)

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Book Synopsis Groups, Modules, and Model Theory - Surveys and Recent Developments by : Manfred Droste

Download or read book Groups, Modules, and Model Theory - Surveys and Recent Developments written by Manfred Droste and published by Springer. This book was released on 2017-06-02 with total page 493 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume focuses on group theory and model theory with a particular emphasis on the interplay of the two areas. The survey papers provide an overview of the developments across group, module, and model theory while the research papers present the most recent study in those same areas. With introductory sections that make the topics easily accessible to students, the papers in this volume will appeal to beginning graduate students and experienced researchers alike. As a whole, this book offers a cross-section view of the areas in group, module, and model theory, covering topics such as DP-minimal groups, Abelian groups, countable 1-transitive trees, and module approximations. The papers in this book are the proceedings of the conference “New Pathways between Group Theory and Model Theory,” which took place February 1-4, 2016, in Mülheim an der Ruhr, Germany, in honor of the editors’ colleague Rüdiger Göbel. This publication is dedicated to Professor Göbel, who passed away in 2014. He was one of the leading experts in Abelian group theory.

Modules over Discrete Valuation Domains

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Publisher : Walter de Gruyter
ISBN 13 : 3110205785
Total Pages : 369 pages
Book Rating : 4.1/5 (12 download)

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Book Synopsis Modules over Discrete Valuation Domains by : Piotr A. Krylov

Download or read book Modules over Discrete Valuation Domains written by Piotr A. Krylov and published by Walter de Gruyter. This book was released on 2008-08-27 with total page 369 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Invariance of Modules under Automorphisms of their Envelopes and Covers

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Publisher : Cambridge University Press
ISBN 13 : 1108949533
Total Pages : 235 pages
Book Rating : 4.1/5 (89 download)

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Book Synopsis Invariance of Modules under Automorphisms of their Envelopes and Covers by : Ashish K. Srivastava

Download or read book Invariance of Modules under Automorphisms of their Envelopes and Covers written by Ashish K. Srivastava and published by Cambridge University Press. This book was released on 2021-03-18 with total page 235 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides a unified treatment of the study of modules invariant under automorphisms of their envelopes and covers.

Abelian Groups, Rings, Modules, and Homological Algebra

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Publisher : CRC Press
ISBN 13 : 9781584885528
Total Pages : 368 pages
Book Rating : 4.8/5 (855 download)

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Book Synopsis Abelian Groups, Rings, Modules, and Homological Algebra by : Pat Goeters

Download or read book Abelian Groups, Rings, Modules, and Homological Algebra written by Pat Goeters and published by CRC Press. This book was released on 2006-01-27 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 participants of these talks along with contributions from other veteran researchers who were unable to attend. These papers reflect many of the current topics in Abelian Groups, Commutative Algebra, Commutative Rings, Group Theory, Homological Algebra, Lie Algebras, and Module Theory. Accessible even to beginning mathematicians, many of these articles suggest problems and programs for future study. This volume is an outstanding addition to the literature and a valuable handbook for beginning as well as seasoned researchers in Algebra. about the editors... H. PAT GOETERS completed his undergraduate studies in mathematics and computer science at Southern Connecticut State University and received his Ph.D. in 1984 from the University of Connecticut under the supervision of William J. Wickless. After spending one year in a post-doctoral position in Wesleyan University under the tutelage of James D. Reid, Goeters was invited for a tenure track position in Auburn University by Ulrich F. Albrecht. Soon afterwards, William Ullery and Overtoun Jenda were hired, and so began a lively Algebra group. OVERTOUN M. G. JENDA received his bachelor's degree in Mathematics from Chancellor College, the University of Malawi. He moved to the U.S. 1977 to pursue graduate studies at University of Kentucky, earning his Ph.D. in 1981 under the supervision of Professor Edgar Enochs. He then returned to Chancellor College, where he was a lecturer (assistant professor) for three years. He moved to the University of Botswana for another three-year stint as a lecturer before moving back to the University of Kentucky as a visiting assistant professor in 1987. In 1988, he joined the Algebra research group at Auburn University.

Advances in Representation Theory of Algebras

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Publisher : American Mathematical Soc.
ISBN 13 : 147045159X
Total Pages : 257 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Advances in Representation Theory of Algebras by : Ibrahim Assem

Download or read book Advances in Representation Theory of Algebras written by Ibrahim Assem and published by American Mathematical Soc.. This book was released on 2021-01-06 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Seventh ARTA (“Advances in Representation Theory of Algebras VII”) conference took place at the Instituto de Matemáticas of the Universidad Nacional Autónoma de México, in Mexico City, from September 24–28, 2018, in honor of José Antonio de la Peña's 60th birthday. Papers in this volume cover topics Professor de la Peña worked on, such as covering theory, tame algebras, and the use of quadratic forms in representation theory. Also included are papers on the categorical approach to representations of algebras and relations to Lie theory, Cohen–Macaulay modules, quantum groups and other algebraic structures.

Rings, Polynomials, and Modules

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Publisher : Springer
ISBN 13 : 3319658743
Total Pages : 374 pages
Book Rating : 4.3/5 (196 download)

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Book Synopsis Rings, Polynomials, and Modules by : Marco Fontana

Download or read book Rings, Polynomials, and Modules written by Marco Fontana and published by Springer. This book was released on 2017-11-11 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents a collection of articles highlighting recent developments in commutative algebra and related non-commutative generalizations. It also includes an extensive bibliography and lists a substantial number of open problems that point to future directions of research in the represented subfields. The contributions cover areas in commutative algebra that have flourished in the last few decades and are not yet well represented in book form. Highlighted topics and research methods include Noetherian and non-Noetherian ring theory, module theory and integer-valued polynomials along with connections to algebraic number theory, algebraic geometry, topology and homological algebra. Most of the eighteen contributions are authored by attendees of the two conferences in commutative algebra that were held in the summer of 2016: “Recent Advances in Commutative Ring and Module Theory,” Bressanone, Italy; “Conference on Rings and Polynomials” Graz, Austria. There is also a small collection of invited articles authored by experts in the area who could not attend either of the conferences. Following the model of the talks given at these conferences, the volume contains a number of comprehensive survey papers along with related research articles featuring recent results that have not yet been published elsewhere.

Advances in Rings and Modules

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Publisher : American Mathematical Soc.
ISBN 13 : 1470435551
Total Pages : 298 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Advances in Rings and Modules by : Sergio R. López-Permouth

Download or read book Advances in Rings and Modules written by Sergio R. López-Permouth and published by American Mathematical Soc.. This book was released on 2018-09-06 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume, dedicated to Bruno J. Müller, a renowned algebraist, is a collection of papers that provide a snapshot of the diversity of themes and applications that interest algebraists today. The papers highlight the latest progress in ring and module research and present work done on the frontiers of the topics discussed. In addition, selected expository articles are included to give algebraists and other mathematicians, including graduate students, an accessible introduction to areas that may be outside their own expertise.

Almost Free Modules

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Publisher : Elsevier
ISBN 13 : 0080527051
Total Pages : 620 pages
Book Rating : 4.0/5 (85 download)

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Book Synopsis Almost Free Modules by : P.C. Eklof

Download or read book Almost Free Modules written by P.C. Eklof and published by Elsevier. This book was released on 2002-04-29 with total page 620 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a comprehensive exposition of the use of set-theoretic methods in abelian group theory, module theory, and homological algebra, including applications to Whitehead's Problem, the structure of Ext and the existence of almost-free modules over non-perfect rings. This second edition is completely revised and udated to include major developments in the decade since the first edition. Among these are applications to cotorsion theories and covers, including a proof of the Flat Cover Conjecture, as well as the use of Shelah's pcf theory to constuct almost free groups. As with the first edition, the book is largely self-contained, and designed to be accessible to both graduate students and researchers in both algebra and logic. They will find there an introduction to powerful techniques which they may find useful in their own work.

Commutative Algebra

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Publisher : Springer Science & Business Media
ISBN 13 : 144196990X
Total Pages : 491 pages
Book Rating : 4.4/5 (419 download)

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Book Synopsis Commutative Algebra by : Marco Fontana

Download or read book Commutative Algebra written by Marco Fontana and published by Springer Science & Business Media. This book was released on 2010-09-29 with total page 491 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Categorical, Homological and Combinatorial Methods in Algebra

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Publisher : American Mathematical Soc.
ISBN 13 : 1470443686
Total Pages : 357 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Categorical, Homological and Combinatorial Methods in Algebra by : Ashish K. Srivastava

Download or read book Categorical, Homological and Combinatorial Methods in Algebra written by Ashish K. Srivastava and published by American Mathematical Soc.. This book was released on 2020-06-23 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains the proceedings of the AMS Special Session, in honor of S. K. Jain's 80th birthday, on Categorical, Homological and Combinatorial Methods in Algebra held from March 16–18, 2018, at Ohio State University, Columbus, Ohio. The articles contained in this volume aim to showcase the current state of art in categorical, homological and combinatorial aspects of algebra.

Foundations of Commutative Rings and Their Modules

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Publisher : Springer Nature
ISBN 13 : 9819752841
Total Pages : 862 pages
Book Rating : 4.8/5 (197 download)

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Book Synopsis Foundations of Commutative Rings and Their Modules by : Fanggui Wang

Download or read book Foundations of Commutative Rings and Their Modules written by Fanggui Wang and published by Springer Nature. This book was released on with total page 862 pages. Available in PDF, EPUB and Kindle. Book excerpt: