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Author : Delmar L. Boyer
Publisher :
ISBN 13 :
Total Pages : 46 pages
Book Rating : 4.0/5 ( download)
Download or read book Enumeration Theorems in Infinite Abelian Groups written by Delmar L. Boyer and published by . This book was released on 1955 with total page 46 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Irving Kaplansky
Publisher : Courier Dover Publications
ISBN 13 : 0486836452
Total Pages : 112 pages
Book Rating : 4.4/5 (868 download)
Download or read book Infinite Abelian Groups written by Irving Kaplansky and published by Courier Dover Publications. This book was released on 2018-12-19 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt: This concise monograph presents the theory of infinite abelian groups in a convenient form and helps students acquire some of the techniques used in modern infinite algebra. 1969 edition.
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 : Jeremy S. Goodman
Publisher :
ISBN 13 :
Total Pages : 49 pages
Book Rating : 4.:/5 (823 download)
Download or read book Structure Theorems for Infinite Abelian Groups written by Jeremy S. Goodman and published by . This book was released on 2012 with total page 49 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abelian groups can be examined according to their structure. One of the structures we will investigate is that of finitely generated abelian groups. In particular, the fundamental theorem for finite abelian groups states they can be expressed as a direct sum of primary cyclic groups. These decompositions are not necessarily unique, however they will have the same invariant factors. Similarly, there is a fundamental theorem for finitely generated abelian groups states that these groups can be decomposed into a direct sum of finitely many cyclic subgroups. However, these subgroups can be finite (cyclic p-groups) or infinite (copies of ([double Z], +)). Just as with finite groups, uniqueness is not achieved, but different decompositions will be isomorphic. This means the number of infinite cyclic summands will be the same, as well as the orders of the primary cyclic summands, which define the invariants of the finitely generated abelian group. The property of being finitely generated is closed under sums, subgroups, and quotients. Two important special classes of infinite abelian groups are torsion groups and torsion-free groups. Every torsion group splits into a direct sum of primary groups, and this decomposition is unique. Every quotient group of an abelian group by its torsion subgroup is torsion-free group. So, every abelian group is an extension of a torsion-free group by a torsion group. This extension does not always split, but there are cases in which it does. For example, the torsion subgroup of a finitely generated abelian group is a direct summand. Another example where the extension splits is with divisible abelian groups. Divisible abelian groups can be decomposed into a direct sum of groups isomorphic to the rationals and p[infinity] groups for various primes p. Divisibility is closed under subgroups, quotients, direct products and sums.
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 : László Fuchs
Publisher :
ISBN 13 :
Total Pages : 384 pages
Book Rating : 4.:/5 (31 download)
Download or read book Infinite Abelian Groups written by László Fuchs and published by . This book was released on 1970 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Vyacheslav L. Girko
Publisher : Academic Press
ISBN 13 : 0080873499
Total Pages : 375 pages
Book Rating : 4.0/5 (88 download)
Download or read book Spectral Theory of Random Matrices written by Vyacheslav L. Girko and published by Academic Press. This book was released on 2016-08-23 with total page 375 pages. Available in PDF, EPUB and Kindle. Book excerpt: Spectral Theory of Random Matrices
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 : Alan Cutler
Publisher :
ISBN 13 :
Total Pages : 40 pages
Book Rating : 4.:/5 (772 download)
Download or read book Structure Theorems for Infinite Abelian Groups written by Alan Cutler and published by . This book was released on 1966 with total page 40 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 : 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 : 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 : Steven R. Finch
Publisher : Cambridge University Press
ISBN 13 : 9780521818056
Total Pages : 634 pages
Book Rating : 4.8/5 (18 download)
Download or read book Mathematical Constants written by Steven R. Finch and published by Cambridge University Press. This book was released on 2003-08-18 with total page 634 pages. Available in PDF, EPUB and Kindle. Book excerpt: Steven Finch provides 136 essays, each devoted to a mathematical constant or a class of constants, from the well known to the highly exotic. This book is helpful both to readers seeking information about a specific constant, and to readers who desire a panoramic view of all constants coming from a particular field, for example, combinatorial enumeration or geometric optimization. Unsolved problems appear virtually everywhere as well. This work represents an outstanding scholarly attempt to bring together all significant mathematical constants in one place.
Author : Brian Donald Wick
Publisher :
ISBN 13 :
Total Pages : 134 pages
Book Rating : 4.:/5 (196 download)
Download or read book Classification Theorems for Infinite Abelian Groups written by Brian Donald Wick and published by . This book was released on 1972 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
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 : S. Barry Cooper
Publisher : Springer Science & Business Media
ISBN 13 : 3540730001
Total Pages : 842 pages
Book Rating : 4.5/5 (47 download)
Download or read book Computation and Logic in the Real World written by S. Barry Cooper and published by Springer Science & Business Media. This book was released on 2007-06-11 with total page 842 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the Third International Conference on Computability in Europe, CiE 2007, held in Sienna, Italy, in June 2007. The 50 revised full papers presented together with 36 invited papers were carefully reviewed and selected from 167 submissions.
