Read Books Online and Download eBooks, EPub, PDF, Mobi, Kindle, Text Full Free.
Modules Over Endomorphism Rings
Download Modules Over Endomorphism Rings full books in PDF, epub, and Kindle. Read online Modules Over Endomorphism Rings ebook anywhere anytime directly on your device. Fast Download speed and no annoying ads. We cannot guarantee that every ebooks is available!
Book Synopsis Categories of Modules over Endomorphism Rings by : Theodore Gerard Faticoni
Download or read book Categories of Modules over Endomorphism Rings written by Theodore Gerard Faticoni and published by American Mathematical Soc.. This book was released on 1993 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is the goal of the memoir to develop a functorial transfer of properties between [italic capital]A and [script capital]M[subscript italic capital]E, the category of modules over [italic capital]E, that is more sensitive than the traditional starting point, Hom([italic capital]A, ·). This memoir should be accessible to anyone who has a working knowledge of rings, modules, functors, and categories equivalent to that gained by reading Anderson and Fuller's text "Rings and Categories of Modules."
Download or read book Module Theory written by Alberto Facchini and published by Springer Science & Business Media. This book was released on 2012-02-03 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents topics in module theory and ring theory: some, such as Goldie dimension and semiperfect rings are now considered classical and others more specialized, such as dual Goldie dimension, semilocal endomorphism rings, serial rings and modules.
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.
Book Synopsis Endomorphism Rings of Abelian Groups by : Piotr A. Krylov
Download or read book Endomorphism Rings of Abelian Groups written by Piotr A. Krylov and published by Springer Science & Business Media. This book was released on 2003-07-31 with total page 460 pages. Available in PDF, EPUB and Kindle. Book excerpt: Every Abelian group can be related to an associative ring with an identity element, the ring of all its endomorphisms. Recently the theory of endomor phism rings of Abelian groups has become a rapidly developing area of algebra. On the one hand, it can be considered as a part of the theory of Abelian groups; on the other hand, the theory can be considered as a branch of the theory of endomorphism rings of modules and the representation theory of rings. There are several reasons for studying endomorphism rings of Abelian groups: first, it makes it possible to acquire additional information about Abelian groups themselves, to introduce new concepts and methods, and to find new interesting classes of groups; second, it stimulates further develop ment of the theory of modules and their endomorphism rings. The theory of endomorphism rings can also be useful for studies of the structure of additive groups of rings, E-modules, and homological properties of Abelian groups. The books of Baer [52] and Kaplansky [245] have played an important role in the early development of the theory of endomorphism rings of Abelian groups and modules. Endomorphism rings of Abelian groups are much stu died in monographs of Fuchs [170], [172], and [173]. Endomorphism rings are also studied in the works of Kurosh [287], Arnold [31], and Benabdallah [63].
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 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: "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.
Download or read book Modules and Rings written by John Dauns and published by Cambridge University Press. This book was released on 1994-10-28 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book on modern module and non-commutative ring theory is ideal for beginning graduate students. It starts at the foundations of the subject and progresses rapidly through the basic concepts to help the reader reach current research frontiers. Students will have the chance to develop proofs, solve problems, and to find interesting questions. The first half of the book is concerned with free, projective, and injective modules, tensor algebras, simple modules and primitive rings, the Jacobson radical, and subdirect products. Later in the book, more advanced topics, such as hereditary rings, categories and functors, flat modules, and purity are introduced. These later chapters will also prove a useful reference for researchers in non-commutative ring theory. Enough background material (including detailed proofs) is supplied to give the student a firm grounding in the subject.
Book Synopsis Foundations of Module and Ring Theory by : Robert Wisbauer
Download or read book Foundations of Module and Ring Theory written by Robert Wisbauer and published by Routledge. This book was released on 2018-05-11 with total page 622 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume provides a comprehensive introduction to module theory and the related part of ring theory, including original results as well as the most recent work. It is a useful and stimulating study for those new to the subject as well as for researchers and serves as a reference volume. Starting form a basic understanding of linear algebra, the theory is presented and accompanied by complete proofs. For a module M, the smallest Grothendieck category containing it is denoted by o[M] and module theory is developed in this category. Developing the techniques in o[M] is no more complicated than in full module categories and the higher generality yields significant advantages: for example, module theory may be developed for rings without units and also for non-associative rings. Numerous exercises are included in this volume to give further insight into the topics covered and to draw attention to related results in the literature.
Book Synopsis Rings and Categories of Modules by : Frank W. Anderson
Download or read book Rings and Categories of Modules written by Frank W. Anderson and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended to provide a reasonably self-contained account of a major portion of the general theory of rings and modules suitable as a text for introductory and more advanced graduate courses. We assume the famil iarity with rings usually acquired in standard undergraduate algebra courses. Our general approach is categorical rather than arithmetical. The continuing theme of the text is the study of the relationship between the one-sided ideal structure that a ring may possess and the behavior of its categories of modules. Following a brief outline of set-theoretic and categorical foundations, the text begins with the basic definitions and properties of rings, modules and homomorphisms and ranges through comprehensive treatments of direct sums, finiteness conditions, the Wedderburn-Artin Theorem, the Jacobson radical, the hom and tensor functions, Morita equivalence and duality, de composition theory of injective and projective modules, and semi perfect and perfect rings. In this second edition we have included a chapter containing many of the classical results on artinian rings that have hdped to form the foundation for much of the contemporary research on the representation theory of artinian rings and finite dimensional algebras. Both to illustrate the text and to extend it we have included a substantial number of exercises covering a wide spectrum of difficulty. There are, of course" many important areas of ring and module theory that the text does not touch upon.
Book Synopsis Rings, Modules, and the Total by : Friedrich Kasch
Download or read book Rings, Modules, and the Total written by Friedrich Kasch and published by Springer Science & Business Media. This book was released on 2004-06-25 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt: Accessible to anyone with a basic knowledge of ring and module theory A short introduction to torsion-free Abelian groups is included
Book Synopsis Linear Algebra over Commutative Rings by : Bernard R. McDonald
Download or read book Linear Algebra over Commutative Rings written by Bernard R. McDonald and published by CRC Press. This book was released on 2020-11-26 with total page 563 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph arose from lectures at the University of Oklahoma on topics related to linear algebra over commutative rings. It provides an introduction of matrix theory over commutative rings. The monograph discusses the structure theory of a projective module.
Book Synopsis Methods of Representation Theory by : Charles W. Curtis
Download or read book Methods of Representation Theory written by Charles W. Curtis and published by Wiley-Interscience. This book was released on 1990-02-01 with total page 848 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 338 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
Download or read book Algebra written by I. Martin Isaacs and published by American Mathematical Soc.. This book was released on 2009 with total page 531 pages. Available in PDF, EPUB and Kindle. Book excerpt: as a student." --Book Jacket.
Book Synopsis A Primer of Algebraic D-Modules by : S. C. Coutinho
Download or read book A Primer of Algebraic D-Modules written by S. C. Coutinho and published by Cambridge University Press. This book was released on 1995-09-07 with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of D-modules is a rich area of study combining ideas from algebra and differential equations, and it has significant applications to diverse areas such as singularity theory and representation theory. This book introduces D-modules and their applications avoiding all unnecessary over-sophistication. It is aimed at beginning graduate students and the approach taken is algebraic, concentrating on the role of the Weyl algebra. Very few prerequisites are assumed, and the book is virtually self-contained. Exercises are included at the end of each chapter and the reader is given ample references to the more advanced literature. This is an excellent introduction to D-modules for all who are new to this area.
Book Synopsis Exercises in Modules and Rings by : T.Y. Lam
Download or read book Exercises in Modules and Rings written by T.Y. Lam and published by Springer Science & Business Media. This book was released on 2009-12-08 with total page 427 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume offers a compendium of exercises of varying degree of difficulty in the theory of modules and rings. It is the companion volume to GTM 189. All exercises are solved in full detail. Each section begins with an introduction giving the general background and the theoretical basis for the problems that follow.
Book Synopsis Arithmetical Rings and Endomorphisms by : Askar A. Tuganbaev
Download or read book Arithmetical Rings and Endomorphisms written by Askar A. Tuganbaev and published by de Gruyter. This book was released on 2019 with total page 0 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.
Book Synopsis Integral Closure of Ideals, Rings, and Modules by : Craig Huneke
Download or read book Integral Closure of Ideals, Rings, and Modules written by Craig Huneke and published by Cambridge University Press. This book was released on 2006-10-12 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ideal for graduate students and researchers, this book presents a unified treatment of the central notions of integral closure.
