Endomorphism Rings Of Abelian Groups
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Endomorphism Rings Of Abelian Groups
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Author : P.A. Krylov
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Endomorphism Rings Of Abelian Groups written by P.A. Krylov 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 2013-06-29 with Mathematics categories.
Every Abelian group can be related to an associative ring with an identity element, the ring of all its endomorphisms. Recently the theory of endomor phism rings of Abelian groups has become a rapidly developing area of algebra. On the one hand, it can be considered as a part of the theory of Abelian groups; on the other hand, the theory can be considered as a branch of the theory of endomorphism rings of modules and the representation theory of rings. There are several reasons for studying endomorphism rings of Abelian groups: first, it makes it possible to acquire additional information about Abelian groups themselves, to introduce new concepts and methods, and to find new interesting classes of groups; second, it stimulates further develop ment of the theory of modules and their endomorphism rings. The theory of endomorphism rings can also be useful for studies of the structure of additive groups of rings, E-modules, and homological properties of Abelian groups. The books of Baer [52] and Kaplansky [245] have played an important role in the early development of the theory of endomorphism rings of Abelian groups and modules. Endomorphism rings of Abelian groups are much stu died in monographs of Fuchs [170], [172], and [173]. Endomorphism rings are also studied in the works of Kurosh [287], Arnold [31], and Benabdallah [63].
Endomorphism Rings Of Abelian Groups
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Author : P. A. Krylov
language : en
Publisher:
Release Date : 2014-01-15
Endomorphism Rings Of Abelian Groups written by P. A. Krylov and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
Finite Rank Torsion Free Abelian Groups And Rings
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Author : D. M. Arnold
language : en
Publisher: Springer
Release Date : 2006-11-14
Finite Rank Torsion Free Abelian Groups And Rings written by D. M. Arnold and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
Abelian Groups
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Author : L. Fuchs
language : en
Publisher: Elsevier
Release Date : 2014-07-15
Abelian Groups written by L. Fuchs and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-15 with Mathematics categories.
Abelian Groups deals with the theory of abelian or commutative groups, with special emphasis on results concerning structure problems. More than 500 exercises of varying degrees of difficulty, with and without hints, are included. Some of the exercises illuminate the theorems cited in the text by providing alternative developments, proofs or counterexamples of generalizations. Comprised of 16 chapters, this volume begins with an overview of the basic facts on group theory such as factor group or homomorphism. The discussion then turns to direct sums of cyclic groups, divisible groups, and direct summands and pure subgroups, as well as Kulikov's basic subgroups. Subsequent chapters focus on the structure theory of the three main classes of abelian groups: the primary groups, the torsion-free groups, and the mixed groups. Applications of the theory are also considered, along with other topics such as homomorphism groups and endomorphism rings; the Schreier extension theory with a discussion of the group of extensions and the structure of the tensor product. In addition, the book examines the theory of the additive group of rings and the multiplicative group of fields, along with Baer's theory of the lattice of subgroups. This book is intended for young research workers and students who intend to familiarize themselves with abelian groups.
Abelian Groups Rings Modules And Homological Algebra
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Author : Pat Goeters
language : en
Publisher: CRC Press
Release Date : 2016-04-19
Abelian Groups Rings Modules And Homological Algebra written by Pat Goeters and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-04-19 with Mathematics categories.
About the book In honor of Edgar Enochs and his venerable contributions to a broad range of topics in Algebra, top researchers from around the world gathered at Auburn University to report on their latest work and exchange ideas on some of today's foremost research topics. This carefully edited volume presents the refereed papers of the par
Abelian Groups Rings And Modules
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Author : Andrei V. Kelarev
language : en
Publisher: American Mathematical Soc.
Release Date : 2001
Abelian Groups Rings And Modules written by Andrei V. Kelarev 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 2001 with Mathematics categories.
This volume presents the proceedings from the conference on Abelian Groups, Rings, and Modules (AGRAM) held at the University of Western Australia (Perth). Included are articles based on talks given at the conference, as well as a few specially invited papers. The proceedings were dedicated to Professor László Fuchs. The book includes a tribute and a review of his work by his long-time collaborator, Professor Luigi Salce. Four surveys from leading experts follow Professor Salce's article. They present recent results from active research areas
Abelian Group Theory
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Author : Rüdiger Göbel
language : en
Publisher: CRC Press
Release Date : 1987
Abelian Group Theory written by Rüdiger Göbel and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with Mathematics categories.
Module Theory
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Author : Alberto Facchini
language : en
Publisher: Birkhäuser
Release Date : 2013-11-27
Module Theory written by Alberto Facchini and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-27 with Mathematics categories.
This expository monograph was written for three reasons. Firstly, we wanted to present the solution to a problem posed by Wolfgang Krull in 1932 [Krull 32]. He asked whether what we now call the "Krull-Schmidt Theorem" holds for ar tinian modules. The problem remained open for 63 years: its solution, a negative answer to Krull's question, was published only in 1995 (see [Facchini, Herbera, Levy and Vamos]). Secondly, we wanted to present the answer to a question posed by Warfield in 1975 [Warfield 75]. He proved that every finitely pre sented module over a serial ring is a direct sum of uniserial modules, and asked if such a decomposition was unique. In other words, Warfield asked whether the "Krull-Schmidt Theorem" holds for serial modules. The solution to this problem, a negative answer again, appeared in [Facchini 96]. Thirdly, the so lution to Warfield's problem shows interesting behavior, a rare phenomenon in the history of Krull-Schmidt type theorems. Essentially, the Krull-Schmidt Theorem holds for some classes of modules and not for others. When it does hold, any two indecomposable decompositions are uniquely determined up to a permutation, and when it does not hold for a class of modules, this is proved via an example. For serial modules the Krull-Schmidt Theorem does not hold, but any two indecomposable decompositions are uniquely determined up to two permutations. We wanted to present such a phenomenon to a wider math ematical audience.
Semilocal Categories And Modules With Semilocal Endomorphism Rings
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Author : Alberto Facchini
language : en
Publisher: Springer Nature
Release Date : 2019-10-23
Semilocal Categories And Modules With Semilocal Endomorphism Rings written by Alberto Facchini and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-10-23 with Mathematics categories.
This book collects and coherently presents the research that has been undertaken since the author’s previous book Module Theory (1998). In addition to some of the key results since 1995, it also discusses the development of much of the supporting material. In the twenty years following the publication of the Camps-Dicks theorem, the work of Facchini, Herbera, Shamsuddin, Puninski, Prihoda and others has established the study of serial modules and modules with semilocal endomorphism rings as one of the promising directions for module-theoretic research. Providing readers with insights into the directions in which the research in this field is moving, as well as a better understanding of how it interacts with other research areas, the book appeals to undergraduates and graduate students as well as researchers interested in algebra.
Rings Modules And The Total
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Author : Friedrich Kasch
language : en
Publisher: Springer Science & Business Media
Release Date : 2004-06-25
Rings Modules And The Total written by Friedrich Kasch 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 2004-06-25 with Mathematics categories.
Accessible to anyone with a basic knowledge of ring and module theory A short introduction to torsion-free Abelian groups is included