Continuous and Discrete Modules
Continuous and Discrete Modules

Author: Saad H. Mohamed

Publisher: Cambridge University Press

Published: 1990-02-22

Total Pages: 141

ISBN-13: 0521399750

DOWNLOAD EBOOK

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.

Classes of Modules
Classes of Modules

Author: John Dauns

Publisher: CRC Press

Published: 2006-06-19

Total Pages: 232

ISBN-13: 1420011596

DOWNLOAD EBOOK

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

Lifting Modules
Lifting Modules

Author: John Clark

Publisher: Springer Science & Business Media

Published: 2008-08-17

Total Pages: 403

ISBN-13: 3764375736

DOWNLOAD EBOOK

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.

Algebra And Number Theory
Algebra And Number Theory

Author: Mohammed Boulagouaz

Publisher: CRC Press

Published: 1999-11-09

Total Pages: 306

ISBN-13: 9780203903889

DOWNLOAD EBOOK

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

Lectures on Modules and Rings
Lectures on Modules and Rings

Author: Tsit-Yuen Lam

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 577

ISBN-13: 1461205255

DOWNLOAD EBOOK

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.

Extensions of Rings and Modules
Extensions of Rings and Modules

Author: Gary F. Birkenmeier

Publisher: Springer Science & Business Media

Published: 2013-07-19

Total Pages: 442

ISBN-13: 0387927166

DOWNLOAD EBOOK

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.

Exercises in Modules and Rings
Exercises in Modules and Rings

Author: T.Y. Lam

Publisher: Springer Science & Business Media

Published: 2009-12-08

Total Pages: 427

ISBN-13: 0387488995

DOWNLOAD EBOOK

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.

Modules and Algebras
Modules and Algebras

Author: Robert Wisbauer

Publisher: CRC Press

Published: 1996-05-15

Total Pages: 384

ISBN-13: 9780582289819

DOWNLOAD EBOOK

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.

Extending Modules
Extending Modules

Author: Nguyen Viet Dung

Publisher: Routledge

Published: 2019-01-22

Total Pages: 248

ISBN-13: 1351449095

DOWNLOAD EBOOK

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

Modules and Comodules
Modules and Comodules

Author: Tomasz Brzezinski

Publisher: Springer Science & Business Media

Published: 2008-06-26

Total Pages: 355

ISBN-13: 3764387424

DOWNLOAD EBOOK

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.