Algebras And Modules Ii

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Algebras and Modules II

Idun Reiten,Sverre O. Smalø,Øyvind Solberg,Canadian Mathematical Society
Algebras and Modules II Book PDF

Author : Idun Reiten,Sverre O. Smalø,Øyvind Solberg,Canadian Mathematical Society
Publisher : American Mathematical Soc.
Page : 596 pages
File Size : 49,7 Mb
Release : 1998
Category : Mathematics
ISBN : 0821810766

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Algebras and Modules II by Idun Reiten,Sverre O. Smalø,Øyvind Solberg,Canadian Mathematical Society Pdf

The 43 research papers demonstrate the application of recent developments in the representation theory of artin algebras and related topics. Among the algebras considered are tame, bi- serial, cellular, factorial hereditary, Hopf, Koszul, non- polynomial growth, pre-projective, Termperley-Lieb, tilted, and quasi-tilted. Other topics include tilting and co-tilting modules and generalizations as *-modules, exceptional sequences of modules and vector bundles, homological conjectives, and vector space categories. The treatment assumes knowledge of non- commutative algebra, including rings, modules, and homological algebra at a graduate or professional level. No index. Member prices are $79 for institutions and $59 for individuals, which also apply to members of the Canadian Mathematical Society. Annotation copyrighted by Book News, Inc., Portland, OR

Approximations and Endomorphism Algebras of Modules

Rüdiger Göbel,Jan Trlifaj
Approximations and Endomorphism Algebras of Modules Book PDF

Author : Rüdiger Göbel,Jan Trlifaj
Publisher : Walter de Gruyter
Page : 1002 pages
File Size : 50,6 Mb
Release : 2012-10-01
Category : Mathematics
ISBN : 9783110218114

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Approximations and Endomorphism Algebras of Modules by Rüdiger Göbel,Jan Trlifaj Pdf

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.

Algebras, Rings and Modules

Michiel Hazewinkel,Nadiya M. Gubareni
Algebras Rings and Modules Book PDF

Author : Michiel Hazewinkel,Nadiya M. Gubareni
Publisher : CRC Press
Page : 388 pages
File Size : 49,6 Mb
Release : 2016-04-05
Category : Mathematics
ISBN : 9781482245059

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Algebras, Rings and Modules by Michiel Hazewinkel,Nadiya M. Gubareni Pdf

The theory of algebras, rings, and modules is one of the fundamental domains of modern mathematics. General algebra, more specifically non-commutative algebra, is poised for major advances in the twenty-first century (together with and in interaction with combinatorics), just as topology, analysis, and probability experienced in the twentieth century. This volume is a continuation and an in-depth study, stressing the non-commutative nature of the first two volumes of Algebras, Rings and Modules by M. Hazewinkel, N. Gubareni, and V. V. Kirichenko. It is largely independent of the other volumes. The relevant constructions and results from earlier volumes have been presented in this volume.

Algebras, Rings and Modules, Volume 2

Michiel Hazewinkel,Nadiya M. Gubareni
Algebras Rings and Modules Volume 2 Book PDF

Author : Michiel Hazewinkel,Nadiya M. Gubareni
Publisher : CRC Press
Page : 364 pages
File Size : 48,7 Mb
Release : 2017-04-11
Category : Mathematics
ISBN : 9781351869874

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Algebras, Rings and Modules, Volume 2 by Michiel Hazewinkel,Nadiya M. Gubareni Pdf

The theory of algebras, rings, and modules is one of the fundamental domains of modern mathematics. General algebra, more specifically non-commutative algebra, is poised for major advances in the twenty-first century (together with and in interaction with combinatorics), just as topology, analysis, and probability experienced in the twentieth century. This is the second volume of Algebras, Rings and Modules: Non-commutative Algebras and Rings by M. Hazewinkel and N. Gubarenis, a continuation stressing the more important recent results on advanced topics of the structural theory of associative algebras, rings and modules.

Extensions of Rings and Modules

Gary F. Birkenmeier,Jae Keol Park,S Tariq Rizvi
Extensions of Rings and Modules Book PDF

Author : Gary F. Birkenmeier,Jae Keol Park,S Tariq Rizvi
Publisher : Springer Science & Business Media
Page : 442 pages
File Size : 54,9 Mb
Release : 2013-07-19
Category : Mathematics
ISBN : 9780387927169

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Extensions of Rings and Modules by Gary F. Birkenmeier,Jae Keol Park,S Tariq Rizvi Pdf

The "extensions" of rings and modules have yet to be explored in detail in a research monograph. This book presents state of the art research and also stimulating new and further research. Broken into three parts, Part I begins with basic notions, terminology, definitions and a description of the classes of rings and modules. Part II considers the transference of conditions between a base ring or module and its extensions. And Part III utilizes the concept of a minimal essental extension with respect to a specific class (a hull). Mathematical interdisciplinary applications appear throughout. Major applications of the ring and module theory to Functional Analysis, especially C*-algebras, appear in Part III, make this book of interest to Algebra and Functional Analysis researchers. Notes and exercises at the end of every chapter, and open problems at the end of all three parts, lend this as an ideal textbook for graduate or advanced undergradate students.

Model Theory of Modules, Algebras and Categories

Alberto Facchini,Lorna Gregory,Sonia L’Innocente,Marcus Tressl
Model Theory of Modules Algebras and Categories Book PDF

Author : Alberto Facchini,Lorna Gregory,Sonia L’Innocente,Marcus Tressl
Publisher : American Mathematical Soc.
Page : 237 pages
File Size : 52,6 Mb
Release : 2019-05-31
Category : Algebra
ISBN : 9781470443672

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Model Theory of Modules, Algebras and Categories by Alberto Facchini,Lorna Gregory,Sonia L’Innocente,Marcus Tressl Pdf

This volume contains the proceedings of the international conference Model Theory of Modules, Algebras and Categories, held from July 28–August 2, 2017, at the Ettore Majorana Foundation and Centre for Scientific Culture in Erice, Italy. Papers contained in this volume cover recent developments in model theory, module theory and category theory, and their intersection.

Modules and Group Algebras

Jon Carlson
Modules and Group Algebras Book PDF

Author : Jon Carlson
Publisher : Springer Science & Business Media
Page : 108 pages
File Size : 46,7 Mb
Release : 1996-02-29
Category : Mathematics
ISBN : 3764353899

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Modules and Group Algebras by Jon Carlson Pdf

The notes in this volume were written as a part of a Nachdiplom course that I gave at the ETH in the summer semester of 1995. The aim of my lectures was the development of some of the basics of the interaction of homological algebra, or more specifically the cohomology of groups, and modular representation theory. Every time that I had given such a course in the past fifteen years, the choice of the material and the order of presentation of the results have followed more or less the same basic pattern. Such a course began with the fundamentals of group cohomology, and then investigated the structure of cohomology rings, and their maximal ideal spectra. Then the variety of a module was defined and related to actual module structure through the rank variety. Applications followed. The standard approach was used in my University of Essen Lecture Notes [e1] in 1984. Evens [E] and Benson [B2] have written it up in much clearer detail and included it as part of their books on the subject.

Algebra

Falko Lorenz
Algebra Book PDF

Author : Falko Lorenz
Publisher : Springer Science & Business Media
Page : 343 pages
File Size : 51,9 Mb
Release : 2007-12-27
Category : Mathematics
ISBN : 9780387724874

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Algebra by Falko Lorenz Pdf

This is Volume II of a two-volume introductory text in classical algebra. The text moves methodically with numerous examples and details so that readers with some basic knowledge of algebra can read it without difficulty. It is recommended either as a textbook for some particular algebraic topic or as a reference book for consultations in a selected fundamental branch of algebra. The book contains a wealth of material. Amongst the topics covered in Volume are the theory of ordered fields and Nullstellen Theorems. Known researcher Lorenz also includes the fundamentals of the theory of quadratic forms, of valuations, local fields and modules. What’s more, the book contains some lesser known or nontraditional results – for instance, Tsen's results on the solubility of systems of polynomial equations with a sufficiently large number of indeterminates.

Finite Group Algebras and Their Modules

P. Landrock
Finite Group Algebras and Their Modules Book PDF

Author : P. Landrock
Publisher : Cambridge University Press
Page : 287 pages
File Size : 45,8 Mb
Release : 1983-12-29
Category : Mathematics
ISBN : 9780521274876

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Finite Group Algebras and Their Modules by P. Landrock Pdf

This book is concerned with the structure of group algebras of finite groups over fields of characteristic [lowercase italic]p dividing the order of the group, or closely related rings such as rings of algebraic integers and in particular their [lowercase italic]p-adic completions, as well as modules and homomorphisms between them, or such group algebras. Our principal aim has been to present some of the more recent ideas which have enriched and improved this theory. This text is not restricted to particular methods, be they ring theoretic or character theoretic, while presenting approaches or proofs which are distinguished by being fast, elegant, illuminating, with potential for further advancement, or all of these at the same time. This text hopes to attract non-specialists, perhaps algebraic topologists and group theorists who might use the tools of modular representations more frequently.

Algebra

William A. Adkins,Steven H. Weintraub
Algebra Book PDF

Author : William A. Adkins,Steven H. Weintraub
Publisher : Springer Science & Business Media
Page : 540 pages
File Size : 55,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461209232

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Algebra by William A. Adkins,Steven H. Weintraub Pdf

This book is designed as a text for a first-year graduate algebra course. As necessary background we would consider a good undergraduate linear algebra course. An undergraduate abstract algebra course, while helpful, is not necessary (and so an adventurous undergraduate might learn some algebra from this book). Perhaps the principal distinguishing feature of this book is its point of view. Many textbooks tend to be encyclopedic. We have tried to write one that is thematic, with a consistent point of view. The theme, as indicated by our title, is that of modules (though our intention has not been to write a textbook purely on module theory). We begin with some group and ring theory, to set the stage, and then, in the heart of the book, develop module theory. Having developed it, we present some of its applications: canonical forms for linear transformations, bilinear forms, and group representations. Why modules? The answer is that they are a basic unifying concept in mathematics. The reader is probably already familiar with the basic role that vector spaces play in mathematics, and modules are a generaliza tion of vector spaces. (To be precise, modules are to rings as vector spaces are to fields.

Algebras, Rings and Modules

Michiel Hazewinkel,Nadiya Gubareni,V.V. Kirichenko
Algebras Rings and Modules Book PDF

Author : Michiel Hazewinkel,Nadiya Gubareni,V.V. Kirichenko
Publisher : Springer
Page : 0 pages
File Size : 43,9 Mb
Release : 2010-11-30
Category : Mathematics
ISBN : 9048172926

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Algebras, Rings and Modules by Michiel Hazewinkel,Nadiya Gubareni,V.V. Kirichenko Pdf

This second volume of this text covers the classical aspects of the theory of groups and their representations. It also offers a general introduction to the modern theory of representations including the representations of quivers and finite partially ordered sets and their applications to finite dimensional algebras. It reviews key recent developments in the theory of special ring classes including Frobenius, quasi-Frobenius, and others.

Rings, Modules, Algebras, and Abelian Groups

Alberto Facchini,Evan Houston,Luigi Salce
Rings Modules Algebras and Abelian Groups Book PDF

Author : Alberto Facchini,Evan Houston,Luigi Salce
Publisher : CRC Press
Page : 530 pages
File Size : 49,6 Mb
Release : 2020-02-10
Category : Mathematics
ISBN : 0824750810

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Rings, Modules, Algebras, and Abelian Groups by Alberto Facchini,Evan Houston,Luigi Salce Pdf

Rings, Modules, Algebras, and Abelian Groups summarizes the proceedings of a recent algebraic conference held at Venice International University in Italy. Surveying the most influential developments in the field, this reference reviews the latest research on Abelian groups, algebras and their representations, module and ring theory, and topological

Operator Algebras and Their Modules

David P. Blecher,Christian Le Merdy
Operator Algebras and Their Modules Book PDF

Author : David P. Blecher,Christian Le Merdy
Publisher : Clarendon Press
Page : 398 pages
File Size : 47,6 Mb
Release : 2004
Category : Language Arts & Disciplines
ISBN : 0198526598

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Operator Algebras and Their Modules by David P. Blecher,Christian Le Merdy Pdf

This invaluable reference is the first to present the general theory of algebras of operators on a Hilbert space, and the modules over such algebras. The new theory of operator spaces is presented early on and the text assembles the basic concepts, theory and methodologies needed to equip a beginning researcher in this area. A major trend in modern mathematics, inspired largely by physics, is toward `noncommutative' or `quantized' phenomena. In functional analysis, this has appeared notably under the name of `operator spaces', which is a variant of Banach spaces which is particularly appropriate for solving problems concerning spaces or algebras of operators on Hilbert space arising in 'noncommutative mathematics'. The category of operator spaces includes operator algebras, selfadjoint (that is, C*-algebras) or otherwise. Also, most of the important modules over operator algebras are operator spaces. A common treatment of the subjects of C*-algebras, Non-selfadjoint operator algebras, and modules over such algebras (such as Hilbert C*-modules), together under the umbrella of operator space theory, is the main topic of the book. A general theory of operator algebras, and their modules, naturally develops out of the operator space methodology. Indeed, operator space theory is a sensitive enough medium to reflect accurately many important non-commutative phenomena. Using recent advances in the field, the book shows how the underlying operator space structure captures, very precisely, the profound relations between the algebraic and the functional analytic structures involved. The rich interplay between spectral theory, operator theory, C*-algebra and von Neumann algebra techniques, and the influx of important ideas from related disciplines, such as pure algebra, Banach space theory, Banach algebras, and abstract function theory is highlighted. Each chapter ends with a lengthy section of notes containing a wealth of additional information.

Algebras, Rings and Modules

Michiel Hazewinkel,Nadiya Gubareni,V.V. Kirichenko
Algebras Rings and Modules Book PDF

Author : Michiel Hazewinkel,Nadiya Gubareni,V.V. Kirichenko
Publisher : Springer Science & Business Media
Page : 405 pages
File Size : 54,8 Mb
Release : 2007-09-08
Category : Mathematics
ISBN : 9781402051418

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Algebras, Rings and Modules by Michiel Hazewinkel,Nadiya Gubareni,V.V. Kirichenko Pdf

This second volume of this text covers the classical aspects of the theory of groups and their representations. It also offers a general introduction to the modern theory of representations including the representations of quivers and finite partially ordered sets and their applications to finite dimensional algebras. It reviews key recent developments in the theory of special ring classes including Frobenius, quasi-Frobenius, and others.

Induced Modules over Group Algebras

G. Karpilovsky
Induced Modules over Group Algebras Book PDF

Author : G. Karpilovsky
Publisher : Elsevier
Page : 519 pages
File Size : 54,5 Mb
Release : 1990-03-01
Category : Mathematics
ISBN : 0080872727

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Induced Modules over Group Algebras by G. Karpilovsky Pdf

In 1898 Frobenius discovered a construction which, in present terminology, associates with every module of a subgroup the induced module of a group. This construction proved to be of fundamental importance and is one of the basic tools in the entire theory of group representations. This monograph is designed for research mathematicians and advanced graduate students and gives a picture of the general theory of induced modules as it exists at present. Much of the material has until now been available only in research articles. The approach is not intended to be encyclopedic, rather each topic is considered in sufficient depth that the reader may obtain a clear idea of the major results in the area. After establishing algebraic preliminaries, the general facts about induced modules are provided, as well as some of their formal properties, annihilators and applications. The remaining chapters include detailed information on the process of induction from normal subgroups, projective summands of induced modules, some basic results of the Green theory with refinements and extensions, simple induction and restriction pairs and permutation modules. The final chapter is based exclusively on the work of Weiss, presenting a number of applications to the isomorphism problem for group rings.