Abelian Categories with Applications to Rings and Modules PDF Download
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Author: Nicolae Popescu
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 488
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Book Description
Author: Nicolae Popescu
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 488
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Book Description
Author: Pat Goeters
Publisher: CRC Press
ISBN: 142001076X
Category : Mathematics
Languages : en
Pages : 354
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Book Description
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: Marco A. P. Bullones
Publisher: CRC Press
ISBN: 1315353466
Category : Mathematics
Languages : en
Pages : 347
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Book Description
Introduction to Abelian Model Structures and Gorenstein Homological Dimensions provides a starting point to study the relationship between homological and homotopical algebra, a very active branch of mathematics. The book shows how to obtain new model structures in homological algebra by constructing a pair of compatible complete cotorsion pairs related to a specific homological dimension and then applying the Hovey Correspondence to generate an abelian model structure. The first part of the book introduces the definitions and notations of the universal constructions most often used in category theory. The next part presents a proof of the Eklof and Trlifaj theorem in Grothedieck categories and covers M. Hovey’s work that connects the theories of cotorsion pairs and model categories. The final two parts study the relationship between model structures and classical and Gorenstein homological dimensions and explore special types of Grothendieck categories known as Gorenstein categories. As self-contained as possible, this book presents new results in relative homological algebra and model category theory. The author also re-proves some established results using different arguments or from a pedagogical point of view. In addition, he proves folklore results that are difficult to locate in the literature.
Author: Marco A. P. Bullones
Publisher: Chapman & Hall/CRC
ISBN: 9781498725347
Category : Abelian categories
Languages : en
Pages : 0
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Book Description
This book provides a starting point to study the relationship between homological and homotopical algebra. It shows how to obtain new model structures in homological algebra by constructing a pair of compatible complete cotorsion pairs related to a specific homological dimension and then applying the Hovey Correspondence to generate an abelian model structure. The book presents new results in relative homological algebra and model category theory, re-proves some established results, and proves folklore results that are difficult to find in the literature.
Author: P.A. Krylov
Publisher: Springer Science & Business Media
ISBN: 9401703450
Category : Mathematics
Languages : en
Pages : 456
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Book Description
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: Laszlo Fuchs
Publisher: CRC Press
ISBN: 100011676X
Category : Mathematics
Languages : en
Pages : 280
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Book Description
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: L. Fuchs
Publisher: Elsevier
ISBN: 148328090X
Category : Mathematics
Languages : en
Pages : 369
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Book Description
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: Dieter Happel
Publisher:
ISBN: 9781470401603
Category : Artin rings
Languages : en
Pages : 88
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Book Description
Author: Dikran Dikranjan
Publisher: CRC Press
ISBN: 0429530064
Category : Mathematics
Languages : en
Pages : 472
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Book Description
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.
Author: Andrei V. Kelarev
Publisher: American Mathematical Soc.
ISBN: 9780821856093
Category : Mathematics
Languages : en
Pages : 324
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Book Description
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 are dedicated to Professor Laszlo 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: Error correcting codes as ideals in group rings, Duality in module categories, Automorphism groups of abelian groups, and Generalizations of isomorphism in torsion-free abelian groups. In addition to these surveys, the volume contains 22 research articles in diverse areas connected with the themes of the conference. The areas discussed include abelian groups and their endomorphism rings, modules over various rings, commutative and non-commutative ring theory, varieties of groups, and topological aspects of algebra. The book offers a comprehensive source for recent research in this active area of study.
