Continuous and Discrete Modules PDF Download
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Author: Saad H. Mohamed
Publisher: Cambridge University Press
ISBN: 0521399750
Category : Mathematics
Languages : en
Pages : 141
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Book Description
Continuous and discrete modules are, essentially, generalizations of infective and projective modules respectively. Continuous modules provide an appropriate setting for decomposition theory of von Neumann algebras and have important applications to C*-algebras. Discrete modules constitute a dual concept and are related to number theory and algebraic geometry: they possess perfect decomposition properties. The advantage of both types of module is that the Krull-Schmidt theorem can be applied, in part, to them. The authors present here a complete account of the subject and at the same time give a unified picture of the theory. The treatment is essentially self-contained, with background facts being summarized in the first chapter. This book will be useful therefore either to individuals beginning research, or the more experienced worker in algebra and representation theory.
Author: Saad H. Mohamed
Publisher: Cambridge University Press
ISBN: 0521399750
Category : Mathematics
Languages : en
Pages : 141
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Book Description
Continuous and discrete modules are, essentially, generalizations of infective and projective modules respectively. Continuous modules provide an appropriate setting for decomposition theory of von Neumann algebras and have important applications to C*-algebras. Discrete modules constitute a dual concept and are related to number theory and algebraic geometry: they possess perfect decomposition properties. The advantage of both types of module is that the Krull-Schmidt theorem can be applied, in part, to them. The authors present here a complete account of the subject and at the same time give a unified picture of the theory. The treatment is essentially self-contained, with background facts being summarized in the first chapter. This book will be useful therefore either to individuals beginning research, or the more experienced worker in algebra and representation theory.
Author: John Dauns
Publisher: CRC Press
ISBN: 1420011596
Category : Mathematics
Languages : en
Pages : 232
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Book Description
Because traditional ring theory places restrictive hypotheses on all submodules of a module, its results apply only to small classes of already well understood examples. Often, modules with infinite Goldie dimension have finite-type dimension, making them amenable to use with type dimension, but not Goldie dimension. By working with natural classes
Author: John Clark
Publisher: Springer Science & Business Media
ISBN: 3764375736
Category : Mathematics
Languages : en
Pages : 403
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Book Description
Extending modules are generalizations of injective modules and, dually, lifting modules generalize projective supplemented modules. This duality exhibits a certain asymmetry. While the theory of extending modules is well documented in monographs and text books, the purpose of this monograph is to provide a thorough study of supplements and projectivity conditions needed to investigate classes of modules related to lifting modules.
Author: Mohammed Boulagouaz
Publisher: CRC Press
ISBN: 9780203903889
Category : Mathematics
Languages : en
Pages : 306
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Book Description
This study demonstrates the key manipulations surrounding Brauer groups, graded rings, group representations, ideal classes of number fields, p-adic differential equations, and rationality problems of invariant fields - displaying a command of the most advanced methods in algebra. It describes new developments in noncommutative valuation theory and
Author: Tsit-Yuen Lam
Publisher: Springer Science & Business Media
ISBN: 1461205255
Category : Mathematics
Languages : en
Pages : 577
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Book Description
This new book can be read independently from the first volume and may be used for lecturing, seminar- and self-study, or for general reference. It focuses more on specific topics in order to introduce readers to a wealth of basic and useful ideas without the hindrance of heavy machinery or undue abstractions. User-friendly with its abundance of examples illustrating the theory at virtually every step, the volume contains a large number of carefully chosen exercises to provide newcomers with practice, while offering a rich additional source of information to experts. A direct approach is used in order to present the material in an efficient and economic way, thereby introducing readers to a considerable amount of interesting ring theory without being dragged through endless preparatory material.
Author: Gary F. Birkenmeier
Publisher: Springer Science & Business Media
ISBN: 0387927166
Category : Mathematics
Languages : en
Pages : 442
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Book Description
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.
Author: T.Y. Lam
Publisher: Springer Science & Business Media
ISBN: 0387488995
Category : Mathematics
Languages : en
Pages : 427
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Book Description
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.
Author: Robert Wisbauer
Publisher: CRC Press
ISBN: 9780582289819
Category : Mathematics
Languages : en
Pages : 384
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Book Description
Module theory over commutative asociative rings is usually extended to noncommutative associative rings by introducing the category of left (or right) modules. An alternative to this procedure is suggested by considering bimodules. A refined module theory for associative rings is used to investigate the bimodule structure of arbitary algebras and group actions on these algebras.
Author: Nguyen Viet Dung
Publisher: Routledge
ISBN: 1351449095
Category : Mathematics
Languages : en
Pages : 248
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Book Description
Module theory is an important tool for many different branches of mathematics, as well as being an interesting subject in its own right. Within module theory, the concept of injective modules is particularly important. Extending modules form a natural class of modules which is more general than the class of injective modules but retains many of its
Author: Tomasz Brzezinski
Publisher: Springer Science & Business Media
ISBN: 3764387424
Category : Mathematics
Languages : en
Pages : 355
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Book Description
The 23 articles in this volume encompass the proceedings of the International Conference on Modules and Comodules held in Porto (Portugal) in 2006. The conference was dedicated to Robert Wisbauer on the occasion of his 65th birthday. These articles reflect Professor Wisbauer's wide interests and give an overview of different fields related to module theory. While some of these fields have a long tradition, others represented here have emerged in recent years.
