Module Theory Extending Modules And Generalizations

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Module Theory Extending Modules And Generalizations

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Author : Adnan Tercan
language : en
Publisher: Birkhäuser
Release Date : 2016-05-13

Module Theory Extending Modules And Generalizations written by Adnan Tercan and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-05-13 with Mathematics categories.

The main focus of this monograph is to offer a comprehensive presentation of known and new results on various generalizations of CS-modules and CS-rings. Extending (or CS) modules are generalizations of injective (and also semisimple or uniform) modules. While the theory of CS-modules is well documented in monographs and textbooks, results on generalized forms of the CS property as well as dual notions are far less present in the literature. With their work the authors provide a solid background to module theory, accessible to anyone familiar with basic abstract algebra. The focus of the book is on direct sums of CS-modules and classes of modules related to CS-modules, such as relative (injective) ejective modules, (quasi) continuous modules, and lifting modules. In particular, matrix CS-rings are studied and clear proofs of fundamental decomposition results on CS-modules over commutative domains are given, thus complementing existing monographs in this area. Open problems round out the work and establish the basis for further developments in the field. The main text is complemented by a wealth of examples and exercises.

Lifting Modules

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Author : John Clark
language : en
Publisher: Birkhäuser
Release Date : 2008-08-17

Lifting Modules written by John Clark and has been published by Birkhäuser 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.

Lifting Modules

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Author : John Clark
language : en
Publisher: Birkhäuser
Release Date : 2009-09-03

Lifting Modules written by John Clark and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-09-03 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.

Lifting Modules

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Author : John Clark
language : en
Publisher: Birkhäuser
Release Date : 2006-07-18

Lifting Modules written by John Clark and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-07-18 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.

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

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.

Extending Modules

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Author : Nguyen Viet Dung
language : en
Publisher: Halsted Press
Release Date : 1994-11-01

Extending Modules written by Nguyen Viet Dung and has been published by Halsted Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-11-01 with Modules (Algebra) categories.

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.

Advances In Rings And Modules

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Author : Sergio R. López-Permouth
language : en
Publisher: American Mathematical Soc.
Release Date : 2018-09-06

Advances In Rings And Modules written by Sergio R. López-Permouth and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-09-06 with Modules (Algebra) categories.

This volume, dedicated to Bruno J. Müller, a renowned algebraist, is a collection of papers that provide a snapshot of the diversity of themes and applications that interest algebraists today. The papers highlight the latest progress in ring and module research and present work done on the frontiers of the topics discussed. In addition, selected expository articles are included to give algebraists and other mathematicians, including graduate students, an accessible introduction to areas that may be outside their own expertise.

Invariance Of Modules Under Automorphisms Of Their Envelopes And Covers

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Author : Ashish K. Srivastava
language : en
Publisher: Cambridge University Press
Release Date : 2021-03-18

Invariance Of Modules Under Automorphisms Of Their Envelopes And Covers written by Ashish K. Srivastava 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 2021-03-18 with Mathematics categories.

The theory of invariance of modules under automorphisms of their envelopes and covers has opened up a whole new direction in the study of module theory. It offers a new perspective on generalizations of injective, pure-injective and flat-cotorsion modules beyond relaxing conditions on liftings of homomorphisms. This has set off a flurry of work in the area, with hundreds of papers using the theory appearing in the last decade. This book gives the first unified treatment of the topic. The authors are real experts in the area, having played a major part in the breakthrough of this new theory and its subsequent applications. The first chapter introduces the basics of ring and module theory needed for the following sections, making it self-contained and suitable for graduate students. The authors go on to develop and explain their tools, enabling researchers to employ them, extend and simplify known results in the literature and to solve longstanding problems in module theory, many of which are discussed at the end of the book.