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Author : László Fuchs
Publisher :
ISBN 13 :
Total Pages : 154 pages
Book Rating : 4.X/5 (1 download)
Download or read book Abelian P-groups and Mixed Groups written by László Fuchs and published by . This book was released on 1980 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : L. Fuchs
Publisher : Elsevier
ISBN 13 : 148328090X
Total Pages : 369 pages
Book Rating : 4.4/5 (832 download)
Download or read book Abelian Groups written by L. Fuchs and published by Elsevier. This book was released on 2014-07-15 with total page 369 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
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 : Grigore Calugareanu
Publisher : Springer Science & Business Media
ISBN 13 : 9781402011832
Total Pages : 376 pages
Book Rating : 4.0/5 (118 download)
Download or read book Exercises in Abelian Group Theory written by Grigore Calugareanu and published by Springer Science & Business Media. This book was released on 2003-04-30 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first book on Abelian Group Theory (or Group Theory) to cover elementary results in Abelian Groups. It contains comprehensive coverage of almost all the topics related to the theory and is designed to be used as a course book for students at both undergraduate and graduate level. The text caters to students of differing capabilities by categorising the exercises in each chapter according to their level of difficulty starting with simple exercises (marked S1, S2 etc), of medium difficulty (M1, M2 etc) and ending with difficult exercises (D1, D2 etc). Solutions for all of the exercises are included. This book should also appeal to experts in the field as an excellent reference to a large number of examples in Group Theory.
Author : John A. Oppelt
Publisher :
ISBN 13 :
Total Pages : 196 pages
Book Rating : 4.:/5 (11 download)
Download or read book Abelian Groups which are a Direct Sum of P-mixed Groups written by John A. Oppelt and published by . This book was released on 1965 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : László Fuchs
Publisher : American Mathematical Soc.
ISBN 13 : 0821850687
Total Pages : 310 pages
Book Rating : 4.8/5 (218 download)
Download or read book Abelian Group Theory written by László Fuchs and published by American Mathematical Soc.. This book was released on 1989 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: The traditional biennial international conference of abelian group theorists was held in August, 1987 at the University of Western Australia in Perth. With some 40 participants from five continents, the conference yielded a variety of papers indicating the healthy state of the field and showing the significant advances made in many areas since the last such conference in Oberwolfach in 1985. This volume brings together the papers presented at the Perth conference, together with a few others submitted by those unable to attend. The first section of the book is concerned with the structure of $p$-groups. It begins with a survey on H. Ulm's contributions to abelian group theory and related areas and also describes the surprising interaction between set theory and the structure of abelian $p$-groups. Another group of papers focuses on automorphism groups and the endomorphism rings of abelian groups. The book also examines various aspects of torsion-free groups, including the theory of their structure and torsion-free groups with many automorphisms. After one paper on mixed groups, the volume closes with a group of papers dealing with properties of modules which generalize corresponding properties of abelian groups.
Author : R. Göbel
Publisher : Springer
ISBN 13 : 3662215608
Total Pages : 788 pages
Book Rating : 4.6/5 (622 download)
Download or read book Abelian Group Theory written by R. Göbel and published by Springer. This book was released on 2013-11-11 with total page 788 pages. Available in PDF, EPUB and Kindle. Book excerpt: A conference on Abelian Group Theory was held at the Manoa Campus of the University of Hawaii from December 28, 1982 to January 4, 1983. It was probably the best attended conference on Abelian Group Theory to date with 55 participants from allover the world and the busiest one with 49 talks. A special feature were general interest lectures by Hyman Bass, Columbia University, on "Non-linear Algebra", and by Claus Michael Ringel, Uni versiUit Bielefeld, on "Representations of Algebras". The Conference offered surveys by Laszlo Fuchs, Tulane University, on "Torsion Modules over Valuation Rings", Fred Richman, New Mexico State University, on "Mixed Groups", Paul Eklof, University of California at Irvine, on "Set Theory and Structure Theorems", Rudiger Gobel, Un:i:versitat Essen on "Endomorphism Rings", and Lee Lady, University of Hawaii, on "Torsion Free Groups of Finite Rank". The research reports attested to lively activity in the traditional and in new areas of inquiry within and around Abelian Group Theory. The best represented groups were those of finite rank without torsion, a field employing increasingly sophisticated tools from ring theory and algebraic number theory. The use of set theoretic methods continues to flourish after the pioneering work of Saharon Shelah in the 1970s, and is delivering impressive results. This volume contains the papers of the participants df the C- ferencean6 a number of additional articles of others who could not or did not corne.
Author : Peter Loth
Publisher : CRC Press
ISBN 13 : 9789056991692
Total Pages : 184 pages
Book Rating : 4.9/5 (916 download)
Download or read book Classifications of Abelian Groups and Pontrjagin Duality written by Peter Loth and published by CRC Press. This book was released on 1998-09-16 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the first part of this book, the reader is introduced to the theory of abelian groups focusing on the classification problem. The structure of totally projective p-groups is determined and Hill's version of Ulm's Theorem is proved. It is shown how this classification theorem is generalized to larger classes of abelian groups such as the balanced projective groups and Warfield groups. A variety of characterizations of these groups is proved generalizing corresponding results for totally projective p-groups. In the second part of this text, the author studies certain classes of compact abelian groups using Pontrjagin duality. After providing the necessary tools for dualization, the structure of the compact groups dual to the totally projective p-groups, balanced projective groups, and Warfield groups is established. Finally, the duals of completely decomposable groups and Butler groups are studied. Supplemented with numerous exercises and research problems, this book is suitable for graduate students, as well as undergraduate students with a sufficient background in algebra and topology.
Author : R. Göbel
Publisher : Springer
ISBN 13 : 3709128145
Total Pages : 526 pages
Book Rating : 4.7/5 (91 download)
Download or read book Abelian Groups and Modules written by R. Göbel and published by Springer. This book was released on 2014-05-04 with total page 526 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Carol Jacoby
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110427680
Total Pages : 342 pages
Book Rating : 4.1/5 (14 download)
Download or read book Abelian Groups written by Carol Jacoby and published by Walter de Gruyter GmbH & Co KG. This book was released on 2019-07-22 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph covers in a comprehensive manner the current state of classification theory with respect to infinite abelian groups. A wide variety of ways to characterise different classes of abelian groups by invariants, isomorphisms and duality principles are discussed.
Author : Rüdiger Göbel
Publisher : CRC Press
ISBN 13 : 9782881241666
Total Pages : 296 pages
Book Rating : 4.2/5 (416 download)
Download or read book Abelian Group Theory written by Rüdiger Göbel and published by CRC Press. This book was released on 1987 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : K.M. Rangaswamy
Publisher : CRC Press
ISBN 13 : 9780824797898
Total Pages : 434 pages
Book Rating : 4.7/5 (978 download)
Download or read book Abelian Groups and Modules written by K.M. Rangaswamy and published by CRC Press. This book was released on 1996-08-16 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains the proceedings of an international conference on abelian groups and modules held recently in Colorado Springs. Presents the latest developments in abelian groups that have facilitated cross-fertilization of new techniques from diverse areas such as the representation theory of posets, model theory, set theory, and module theory.
Author : Rüdiger Göbel
Publisher : Walter de Gruyter
ISBN 13 : 3110203030
Total Pages : 509 pages
Book Rating : 4.1/5 (12 download)
Download or read book Models, Modules and Abelian Groups written by Rüdiger Göbel and published by Walter de Gruyter. This book was released on 2008-12-10 with total page 509 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a memorial volume dedicated to A. L. S. Corner, previously Professor in Oxford, who published important results on algebra, especially on the connections of modules with endomorphism algebras. The volume contains refereed contributions which are related to the work of Corner. It contains also an unpublished extended paper of Corner himself. A memorial volume with important contributions related to algebra.
Author : D. Arnold
Publisher : Springer
ISBN 13 : 3540370692
Total Pages : 436 pages
Book Rating : 4.5/5 (43 download)
Download or read book Abelian Group Theory written by D. Arnold and published by Springer. This book was released on 2006-11-15 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Laszlo Fuchs
Publisher : CRC Press
ISBN 13 : 100011676X
Total Pages : 280 pages
Book Rating : 4.0/5 (1 download)
Download or read book Abelian Groups written by Laszlo Fuchs and published by CRC Press. This book was released on 2022-01-27 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains information offered at the international conference held in Curacao, Netherlands Antilles. It presents the latest developments in the most active areas of abelian groups, particularly in torsion-free abelian groups.;For both researchers and graduate students, it reflects the current status of abelian group theory.;Abelian Groups discusses: finite rank Butler groups; almost completely decomposable groups; Butler groups of infinite rank; equivalence theorems for torsion-free groups; cotorsion groups; endomorphism algebras; and interactions of set theory and abelian groups.;This volume contains contributions from international experts. It is aimed at algebraists and logicians, research mathematicians, and advanced graduate students in these disciplines.
Author : Paul C. Eklof
Publisher : Birkhäuser
ISBN 13 : 3034875916
Total Pages : 374 pages
Book Rating : 4.0/5 (348 download)
Download or read book Abelian Groups and Modules written by Paul C. Eklof and published by Birkhäuser. This book was released on 2013-04-17 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
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
