Continuous And Discrete Modules

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Continuous And Discrete Modules
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Author : Saad H. Mohamed
language : en
Publisher: Cambridge University Press
Release Date : 1990-02-22
Continuous And Discrete Modules written by Saad H. Mohamed and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990-02-22 with Mathematics categories.
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
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Author : John Dauns
language : en
Publisher: CRC Press
Release Date : 2006-06-19
Classes Of Modules written by John Dauns and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-06-19 with Mathematics categories.
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
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Author : John Clark
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-08-17
Lifting Modules written by John Clark and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-08-17 with Mathematics categories.
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
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Author : Mohammed Boulagouaz
language : en
Publisher: CRC Press
Release Date : 1999-11-09
Algebra And Number Theory written by Mohammed Boulagouaz and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-11-09 with Mathematics categories.
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
Extending Modules
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Author : Nguyen Viet Dung
language : en
Publisher: Routledge
Release Date : 2019-01-22
Extending Modules written by Nguyen Viet Dung and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-01-22 with Mathematics categories.
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
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Author : Tomasz Brzezinski
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-06-26
Modules And Comodules written by Tomasz Brzezinski and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-06-26 with Mathematics categories.
The 23 articles in this volume encompass the proceedings of the International Conference on Modules and Comodules held in Porto (Portugal) in 2006 and 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, some of which have a long tradition whereas others have emerged in recent years. They include topics in the formal theory of modules bordering on category theory, in ring theory, in Hopf algebras and quantum groups, and in corings and comodules.
Extensions Of Rings And Modules
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Author : Gary F. Birkenmeier
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-07-19
Extensions Of Rings And Modules written by Gary F. Birkenmeier and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-07-19 with Mathematics categories.
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.
Lectures On Modules And Rings
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Author : Tsit-Yuen Lam
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Lectures On Modules And Rings written by Tsit-Yuen Lam and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Textbook writing must be one of the cruelest of self-inflicted tortures. - Carl Faith Math Reviews 54: 5281 So why didn't I heed the warning of a wise colleague, especially one who is a great expert in the subject of modules and rings? The answer is simple: I did not learn about it until it was too late! My writing project in ring theory started in 1983 after I taught a year-long course in the subject at Berkeley. My original plan was to write up my lectures and publish them as a graduate text in a couple of years. My hopes of carrying out this plan on schedule were, however, quickly dashed as I began to realize how much material was at hand and how little time I had at my disposal. As the years went by, I added further material to my notes, and used them to teach different versions of the course. Eventually, I came to the realization that writing a single volume would not fully accomplish my original goal of giving a comprehensive treatment of basic ring theory. At the suggestion of Ulrike Schmickler-Hirzebruch, then Mathematics Editor of Springer-Verlag, I completed the first part of my project and published the write up in 1991 as A First Course in Noncommutative Rings, GTM 131, hereafter referred to as First Course (or simply FC).
Modules And Algebras
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Author : Robert Wisbauer
language : en
Publisher: CRC Press
Release Date : 1996-05-15
Modules And Algebras written by Robert Wisbauer and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-05-15 with Mathematics categories.
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.
Abelian Groups And Modules
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Author : Paul C. Eklof
language : en
Publisher: Birkhäuser
Release Date : 2013-04-17
Abelian Groups And Modules written by Paul C. Eklof and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Mathematics categories.
A 30-article volume, introducing an active and attractive part of algebra that has gained much from its position at the crossroads of mathematics over the years. The papers stimulate the reader to consider and actively investigate the topics and problems they contain.