Download or read book Abelian Groups Module Theory and Topology written by Dikran Dikranjan and published by CRC Press. This book was released on 2019-05-16 with total page 469 pages. Available in PDF, EPUB and Kindle. Book excerpt: Features a stimulating selection of papers on abelian groups, commutative and noncommutative rings and their modules, and topological groups. Investigates currently popular topics such as Butler groups and almost completely decomposable groups.
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
Download or read book A Course in Homological Algebra written by P.J. Hilton and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this chapter we are largely influenced in our choice of material by the demands of the rest of the book. However, we take the view that this is an opportunity for the student to grasp basic categorical notions which permeate so much of mathematics today, including, of course, algebraic topology, so that we do not allow ourselves to be rigidly restricted by our immediate objectives. A reader totally unfamiliar with category theory may find it easiest to restrict his first reading of Chapter II to Sections 1 to 6; large parts of the book are understandable with the material presented in these sections. Another reader, who had already met many examples of categorical formulations and concepts might, in fact, prefer to look at Chapter II before reading Chapter I. Of course the reader thoroughly familiar with category theory could, in principal, omit Chapter II, except perhaps to familiarize himself with the notations employed. In Chapter III we begin the proper study of homological algebra by looking in particular at the group ExtA(A, B), where A and Bare A-modules. It is shown how this group can be calculated by means of a projective presentation of A, or an injective presentation of B; and how it may also be identified with the group of equivalence classes of extensions of the quotient module A by the submodule B.
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.
Download or read book An Introduction to Homological Algebra written by Charles A. Weibel and published by Cambridge University Press. This book was released on 1995-10-27 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt: The landscape of homological algebra has evolved over the last half-century into a fundamental tool for the working mathematician. This book provides a unified account of homological algebra as it exists today. The historical connection with topology, regular local rings, and semi-simple Lie algebras are also described. This book is suitable for second or third year graduate students. The first half of the book takes as its subject the canonical topics in homological algebra: derived functors, Tor and Ext, projective dimensions and spectral sequences. Homology of group and Lie algebras illustrate these topics. Intermingled are less canonical topics, such as the derived inverse limit functor lim1, local cohomology, Galois cohomology, and affine Lie algebras. The last part of the book covers less traditional topics that are a vital part of the modern homological toolkit: simplicial methods, Hochschild and cyclic homology, derived categories and total derived functors. By making these tools more accessible, the book helps to break down the technological barrier between experts and casual users of homological algebra.
Download or read book Almost Free Modules written by P.C. Eklof and published by Elsevier. This book was released on 2002-04-29 with total page 620 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a comprehensive exposition of the use of set-theoretic methods in abelian group theory, module theory, and homological algebra, including applications to Whitehead's Problem, the structure of Ext and the existence of almost-free modules over non-perfect rings. This second edition is completely revised and udated to include major developments in the decade since the first edition. Among these are applications to cotorsion theories and covers, including a proof of the Flat Cover Conjecture, as well as the use of Shelah's pcf theory to constuct almost free groups. As with the first edition, the book is largely self-contained, and designed to be accessible to both graduate students and researchers in both algebra and logic. They will find there an introduction to powerful techniques which they may find useful in their own work.
Download or read book Abelian Groups and Modules written by Alberto Facchini and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 521 pages. Available in PDF, EPUB and Kindle. Book excerpt: On the 26th of November 1992 the organizing committee gathered together, at Luigi Salce's invitation, for the first time. The tradition of abelian groups and modules Italian conferences (Rome 77, Udine 85, Bressanone 90) needed to be kept up by one more meeting. Since that first time it was clear to us that our goal was not so easy. In fact the main intended topics of abelian groups, modules over commutative rings and non commutative rings have become so specialized in the last years that it looked really ambitious to fit them into only one meeting. Anyway, since everyone of us shared the same mathematical roots, we did want to emphasize a common link. So we elaborated the long symposium schedule: three days of abelian groups and three days of modules over non commutative rings with a two days' bridge of commutative algebra in between. Many of the most famous names in these fields took part to the meeting. Over 140 participants, both attending and contributing the 18 Main Lectures and 64 Communications (see list on page xv) provided a really wide audience for an Algebra meeting. Now that the meeting is over, we can say that our initial feeling was right.
Download or read book Methods of Homological Algebra written by Sergei I. Gelfand and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: This modern approach to homological algebra by two leading writers in the field is based on the systematic use of the language and ideas of derived categories and derived functors. It describes relations with standard cohomology theory and provides complete proofs. Coverage also presents basic concepts and results of homotopical algebra. This second edition contains numerous corrections.
Download or read book Methods of Homological Algebra written by Sergei I. Gelfand and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: Homological algebra first arose as a language for describing topological prospects of geometrical objects. As with every successful language it quickly expanded its coverage and semantics, and its contemporary applications are many and diverse. This modern approach to homological algebra, by two leading writers in the field, is based on the systematic use of the language and ideas of derived categories and derived functors. Relations with standard cohomology theory (sheaf cohomology, spectral sequences, etc.) are described. In most cases complete proofs are given. Basic concepts and results of homotopical algebra are also presented. The book addresses people who want to learn about a modern approach to homological algebra and to use it in their work.
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.
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.
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.
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.
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].
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:
Download or read book Handbook of Algebra written by M. Hazewinkel and published by Elsevier. This book was released on 2000-04-06 with total page 899 pages. Available in PDF, EPUB and Kindle. Book excerpt: Handbook of Algebra
Download or read book Handbook of Algebra written by and published by Elsevier. This book was released on 2003-10-15 with total page 1185 pages. Available in PDF, EPUB and Kindle. Book excerpt: Handbook of Algebra
