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: 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.
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
Advances In Pure And Applied Algebra
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Author : Ratnesh Kumar Mishra
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2023-04-03
Advances In Pure And Applied Algebra written by Ratnesh Kumar Mishra and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-04-03 with Mathematics categories.
This proceedings volume documents the contributions presented at the CONIAPS XXVII International Conference on Recent Advances in Pure and Applied Algebra. The entries focus on modern trends and techniques in various branches of pure and applied Algebra and highlight their applications in coding, cryptography, graph, and fuzzy theory. The book comprised a total of eighteen chapters, among which the first fourteen chapters are devoted to Algebra and related topics, and the last four chapters are included applied mathematics parts. The chapters present the latest research work being done on the frontiers of the various branches of algebra as well as showcase the cross-fertilization of the ideas and connection among these branches.Covering a broad range of topics in pure and applied Algebra, this volume would appeal to a wide spectrum of the researcher in Mathematics. The main aim of this monograph is to contribute to the development of pure and applied Algebra and hence we purposely sought a cross-section of topics in Algebra and encouraged expository presentations and research papers that provide an innovative link between research areas of Algebra and the field of their applications. This volume will be useful not only to experts but also to beginners of research in algebras and related topics.
Groups With Prescribed Quotient Groups And Associated Module Theory
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Author : L. Kurdachenko
language : en
Publisher: World Scientific
Release Date : 2002
Groups With Prescribed Quotient Groups And Associated Module Theory written by L. Kurdachenko and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.
Presents well-established results as well as newer, contemporary achievements in this area from the common integral point of view. This view is based on the implementation of module theory for solving group problems.
Advances In Ring Theory
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Author : S.K. Jain
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Advances In Ring Theory written by S.K. Jain 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.
Exercises In Modules And Rings
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Author : T.Y. Lam
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-12-15
Exercises In Modules And Rings written by T.Y. 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 2006-12-15 with Mathematics categories.
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.
Advances In Ring Theory Proceedings Of The 4th China Japan Korea International Conference
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Author : Jianlong Chen
language : en
Publisher: World Scientific
Release Date : 2005-08-22
Advances In Ring Theory Proceedings Of The 4th China Japan Korea International Conference written by Jianlong Chen and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-08-22 with Mathematics categories.
The selected papers in this volume cover all the most important areas of ring theory and module theory such as classical ring theory, representation theory, the theory of quantum groups, the theory of Hopf algebras, the theory of Lie algebras and Abelian group theory. The review articles, written by specialists, provide an excellent overview of the various areas of ring and module theory — ideal for researchers looking for a new or related field of study. Also included are original articles showing the trend of current research.
Rings Monoids And Module Theory
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Author : Ayman Badawi
language : en
Publisher: Springer Nature
Release Date : 2022-03-11
Rings Monoids And Module Theory written by Ayman Badawi and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-03-11 with Mathematics categories.
This book contains select papers on rings, monoids and module theory which are presented at the 3rd International Conference on Mathematics and Statistics (AUS-ICMS 2020) held at the American University of Sharjah, United Arab Emirates, from 6–9 February 2020. This conference was held in honour of the work of the distinguished algebraist Daniel D. Anderson. Many participants and colleagues from around the world felt it appropriate to acknowledge his broad and sweeping contributions to research in algebra by writing an edited volume in his honor. The topics covered are, inevitably, a cross-section of the vast expansion of modern algebra. The book is divided into two sections—surveys and recent research developments—with each section hopefully offering symbiotic utility to the reader. The book contains a balanced mix of survey papers, which will enable expert and non-expert alike to get a good overview of developments across a range of areas of algebra. The book is expected to be of interest to both beginning graduate students and experienced researchers.
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.