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Author : D. M. Arnold
Publisher : Springer
ISBN 13 : 3540392343
Total Pages : 199 pages
Book Rating : 4.5/5 (43 download)
Download or read book Finite Rank Torsion Free Abelian Groups and Rings written by D. M. Arnold and published by Springer. This book was released on 2006-11-14 with total page 199 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Alberto Facchini
Publisher : CRC Press
ISBN 13 : 9780824750817
Total Pages : 530 pages
Book Rating : 4.7/5 (58 download)
Download or read book Rings, Modules, Algebras, and Abelian Groups written by Alberto Facchini and published by CRC Press. This book was released on 2020-02-10 with total page 530 pages. Available in PDF, EPUB and Kindle. Book excerpt: Rings, Modules, Algebras, and Abelian Groups summarizes the proceedings of a recent algebraic conference held at Venice International University in Italy. Surveying the most influential developments in the field, this reference reviews the latest research on Abelian groups, algebras and their representations, module and ring theory, and topological
Author : David Arnold
Publisher : Springer Science & Business Media
ISBN 13 : 1441987509
Total Pages : 256 pages
Book Rating : 4.4/5 (419 download)
Download or read book Abelian Groups and Representations of Finite Partially Ordered Sets written by David Arnold and published by Springer Science & Business Media. This book was released on 2012-11-14 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theme of this book is an exposition of connections between representations of finite partially ordered sets and abelian groups. Emphasis is placed throughout on classification, a description of the objects up to isomorphism, and computation of representation type, a measure of when classification is feasible. David M. Arnold is the Ralph and Jean Storm Professor of Mathematics at Baylor University. He is the author of "Finite Rank Torsion Free Abelian Groups and Rings" published in the Springer-Verlag Lecture Notes in Mathematics series, a co-editor for two volumes of conference proceedings, and the author of numerous articles in mathematical research journals.
Author : A Mader
Publisher : CRC Press
ISBN 13 : 148228748X
Total Pages : 366 pages
Book Rating : 4.4/5 (822 download)
Download or read book Almost Completely Decomposable Groups written by A Mader and published by CRC Press. This book was released on 2000-03-09 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: An almost completely decomposable abelian (acd) group is an extension of a finite direct sum of subgroups of the additive group of rational numbers by a finite abelian group. Examples are easy to write and are frequently used but have been notoriously difficult to study and classify because of their computational nature. However, a general theory o
Author : László Fuchs
Publisher : Springer
ISBN 13 : 3319194224
Total Pages : 762 pages
Book Rating : 4.3/5 (191 download)
Download or read book Abelian Groups written by László Fuchs and published by Springer. This book was released on 2015-12-12 with total page 762 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by one of the subject’s foremost experts, this book focuses on the central developments and modern methods of the advanced theory of abelian groups, while remaining accessible, as an introduction and reference, to the non-specialist. It provides a coherent source for results scattered throughout the research literature with lots of new proofs. The presentation highlights major trends that have radically changed the modern character of the subject, in particular, the use of homological methods in the structure theory of various classes of abelian groups, and the use of advanced set-theoretical methods in the study of un decidability problems. The treatment of the latter trend includes Shelah’s seminal work on the un decidability in ZFC of Whitehead’s Problem; while the treatment of the former trend includes an extensive (but non-exhaustive) study of p-groups, torsion-free groups, mixed groups and important classes of groups arising from ring theory. To prepare the reader to tackle these topics, the book reviews the fundamentals of abelian group theory and provides some background material from category theory, set theory, topology and homological algebra. An abundance of exercises are included to test the reader’s comprehension, and to explore noteworthy extensions and related sidelines of the main topics. A list of open problems and questions, in each chapter, invite the reader to take an active part in the subject’s further development.
Author : Alberto Facchini
Publisher : Springer Science & Business Media
ISBN 13 : 3034803036
Total Pages : 296 pages
Book Rating : 4.0/5 (348 download)
Download or read book Module Theory written by Alberto Facchini and published by Springer Science & Business Media. This book was released on 2012-02-03 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents topics in module theory and ring theory: some, such as Goldie dimension and semiperfect rings are now considered classical and others more specialized, such as dual Goldie dimension, semilocal endomorphism rings, serial rings and modules.
Author : Piotr A. Krylov
Publisher : Springer Science & Business Media
ISBN 13 : 9781402014383
Total Pages : 460 pages
Book Rating : 4.0/5 (143 download)
Download or read book Endomorphism Rings of Abelian Groups written by Piotr A. Krylov and published by Springer Science & Business Media. This book was released on 2003-07-31 with total page 460 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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].
Author :
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (867 download)
Download or read book Infinite Abelian Groups written by and published by . This book was released on 1954 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Eben Matlis
Publisher : University of Chicago Press
ISBN 13 : 9780226510743
Total Pages : 180 pages
Book Rating : 4.5/5 (17 download)
Download or read book Torsion-Free Modules written by Eben Matlis and published by University of Chicago Press. This book was released on 1972 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: The subject of torsion-free modules over an arbitrary integral domain arises naturally as a generalization of torsion-free abelian groups. In this volume, Eben Matlis brings together his research on torsion-free modules that has appeared in a number of mathematical journals. Professor Matlis has reworked many of the proofs so that only an elementary knowledge of homological algebra and commutative ring theory is necessary for an understanding of the theory. The first eight chapters of the book are a general introduction to the theory of torsion-free modules. This part of the book is suitable for a self-contained basic course on the subject. More specialized problems of finding all integrally closed D-rings are examined in the last seven chapters, where material covered in the first eight chapters is applied. An integral domain is said to be a D-ring if every torsion-free module of finite rank decomposes into a direct sum of modules of rank 1. After much investigation, Professor Matlis found that an integrally closed domain is a D-ring if, and only if, it is the intersection of at most two maximal valuation rings.
Author :
Publisher : Academic Press
ISBN 13 : 0080873480
Total Pages : 305 pages
Book Rating : 4.0/5 (88 download)
Download or read book Infinite Abelian Groups written by and published by Academic Press. This book was released on 1970-01-01 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: Infinite Abelian Groups
Author : Bertram Wehrfritz
Publisher : Springer Science & Business Media
ISBN 13 : 3642870813
Total Pages : 243 pages
Book Rating : 4.6/5 (428 download)
Download or read book Infinite Linear Groups written by Bertram Wehrfritz and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt: By a linear group we mean essentially a group of invertible matrices with entries in some commutative field. A phenomenon of the last twenty years or so has been the increasing use of properties of infinite linear groups in the theory of (abstract) groups, although the story of infinite linear groups as such goes back to the early years of this century with the work of Burnside and Schur particularly. Infinite linear groups arise in group theory in a number of contexts. One of the most common is via the automorphism groups of certain types of abelian groups, such as free abelian groups of finite rank, torsion-free abelian groups of finite rank and divisible abelian p-groups of finite rank. Following pioneering work of Mal'cev many authors have studied soluble groups satisfying various rank restrictions and their automor phism groups in this way, and properties of infinite linear groups now play the central role in the theory of these groups. It has recently been realized that the automorphism groups of certain finitely generated soluble (in particular finitely generated metabelian) groups contain significant factors isomorphic to groups of automorphisms of finitely generated modules over certain commutative Noetherian rings. The results of our Chapter 13, which studies such groups of automorphisms, can be used to give much information here.
Author : Pat Goeters
Publisher : CRC Press
ISBN 13 : 142001076X
Total Pages : 354 pages
Book Rating : 4.4/5 (2 download)
Download or read book Abelian Groups, Rings, Modules, and Homological Algebra written by Pat Goeters and published by CRC Press. This book was released on 2016-04-19 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Author : David M. Arnold
Publisher : Springer Verlag
ISBN 13 : 9780387115573
Total Pages : 191 pages
Book Rating : 4.1/5 (155 download)
Download or read book Finite Rank Torsion Free Abelian Groups and Rings written by David M. Arnold and published by Springer Verlag. This book was released on 1982 with total page 191 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : P.A. Krylov
Publisher : Springer Science & Business Media
ISBN 13 : 9401703450
Total Pages : 456 pages
Book Rating : 4.4/5 (17 download)
Download or read book Endomorphism Rings of Abelian Groups written by P.A. Krylov and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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].
Author : Andrei V. Kelarev
Publisher : American Mathematical Soc.
ISBN 13 : 0821827510
Total Pages : 322 pages
Book Rating : 4.8/5 (218 download)
Download or read book Abelian Groups, Rings and Modules written by Andrei V. Kelarev and published by American Mathematical Soc.. This book was released on 2001 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Author : K. R. Goodearl
Publisher : American Mathematical Soc.
ISBN 13 : 0821849808
Total Pages : 360 pages
Book Rating : 4.8/5 (218 download)
Download or read book Partially Ordered Abelian Groups with Interpolation written by K. R. Goodearl and published by American Mathematical Soc.. This book was released on 2010-05-30 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: A branch of ordered algebraic structures has grown, motivated by $K$-theoretic applications and mainly concerned with partially ordered abelian groups satisfying the Riesz interpolation property. This monograph is the first source in which the algebraic and analytic aspects of these interpolation groups have been integrated into a coherent framework for general reference. The author provides a solid foundation in the structure theory of interpolation groups and dimension groups (directed unperforated interpolation groups), with applications to ordered $K$-theory particularly in mind. Although interpolation groups are defined as purely algebraic structures, their development has been strongly influenced by functional analysis. This cross-cultural development has left interpolation groups somewhat estranged from both the algebraists, who may feel intimidated by compact convex sets, and the functional analysts, who may feel handicapped by the lack of scalars. This book, requiring only standard first-year graduate courses in algebra and functional analysis, aims to make the subject accessible to readers from both disciplines.High points of the development include the following: characterization of dimension groups as direct limits of finite products of copies of the integers; the double-dual representation of an interpolation group with order-unit via affine continuous real-valued functions on its state space; the structure of dimension groups complete with respect to the order-unit norm, as well as monotone sigma-complete dimension groups and dimension groups with countably infinite interpolation; and an introduction to the problem of classifying extensions of one dimension group by another. The book also includes a development of portions of the theory of compact convex sets and Choquet simplices, and an expository discussion of various applications of interpolation group theory to rings and $C DEGREES*$-algebras via ordered $K_0$. A discussion of some open problems in interpolation groups and dimension groups concludes the book.Of interest, of course, to researchers in ordered algebraic structures, the book will also be a valuable source for researchers seeking a background in interpolation groups and dimension groups for applications to such subjects as rings, operator algebras, topological Markov chains, positive polynomials, compact group actions, or other areas where ordered Grothendieck groups might be useful. This is a reprint of the 1986 original. (SUR
Author : D. Valcan
Publisher : Springer Science & Business Media
ISBN 13 : 9401703396
Total Pages : 353 pages
Book Rating : 4.4/5 (17 download)
Download or read book Exercises in Abelian Group Theory written by D. Valcan and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 353 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, in some sense, began to be written by the first author in 1983, when optional lectures on Abelian groups were held at the Fac ulty of Mathematics and Computer Science,'Babes-Bolyai' University in Cluj-Napoca, Romania. From 1992,these lectures were extended to a twosemester electivecourse on abelian groups for undergraduate stu dents, followed by a twosemester course on the same topic for graduate students in Algebra. All the other authors attended these two years of lectures and are now Assistants to the Chair of Algebra of this Fac ulty. The first draft of this collection, including only exercises solved by students as home works, the last ten years, had 160pages. We felt that there is a need for a book such as this one, because it would provide a nice bridge between introductory Abelian Group Theory and more advanced research problems. The book InfiniteAbelianGroups, published by LaszloFuchsin two volumes 1970 and 1973 willwithout doubt last as the most important guide for abelian group theorists. Many exercises are selected from this source but there are plenty of other bibliographical items (see the Bibliography) which were used in order to make up this collection. For some of the problems stated, recent developments are also given. Nevertheless, there are plenty of elementary results (the so called 'folklore') in Abelian Group Theory whichdo not appear in any written material. It is also one purpose of this book to complete this gap.
