Semilocal Categories and Modules with Semilocal Endomorphism Rings, Facchini Alberto

Автор: Alberto Facchini
Название: Semilocal Categories and Modules with Semilocal Endomorphism Rings
ISBN: 3030232832 ISBN-13(EAN): 9783030232832
Издательство: Springer
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Цена: 121110.00 T
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Описание: This book collects and coherently presents the research that has been undertaken since the author’s previous book Module Theory (1998). In addition to some of the key results since 1995, it also discusses the development of much of the supporting material.In the twenty years following the publication of the Camps-Dicks theorem, the work of Facchini, Herbera, Shamsuddin, Puninski, Prihoda and others has established the study of serial modules and modules with semilocal endomorphism rings as one of the promising directions for module-theoretic research.Providing readers with insights into the directions in which the research in this field is moving, as well as a better understanding of how it interacts with other research areas, the book appeals to undergraduates and graduate students as well as researchers interested in algebra.

Автор: R. Baeza
Название: Quadratic Forms Over Semilocal Rings
ISBN: 3540088458 ISBN-13(EAN): 9783540088455
Издательство: Springer
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Цена: 23280.00 T
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Автор: Rudiger Gobel, Jan Trlifaj
Название: Approximations and Endomorphism Algebras of Modules: Volume 1 – Approximations / Volume 2 – Predictions
ISBN: 3110218100 ISBN-13(EAN): 9783110218107
Издательство: Walter de Gruyter
Цена: 358270.00 T
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Описание: 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.

Автор: Rudiger Gobel, Jan Trlifaj
Название: Approximations and Endomorphism Algebras of Modules: Volume 1 – Approximations / Volume 2 – Predictions
ISBN: 3111733203 ISBN-13(EAN): 9783111733203
Издательство: Walter de Gruyter
Цена: 494640.00 T
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Описание: 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.

Автор: P.A. Krylov; Alexander V. Mikhalev; A.A. Tuganbaev
Название: Endomorphism Rings of Abelian Groups
ISBN: 9048163498 ISBN-13(EAN): 9789048163496
Издательство: Springer
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Цена: 93160.00 T
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Описание: 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].

Автор: Askar A. Tuganbaev
Название: Arithmetical Rings and Endomorphisms
ISBN: 3110658895 ISBN-13(EAN): 9783110658897
Издательство: Walter de Gruyter
Цена: 107790.00 T
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Описание: 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.