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Author: A. J. Berrick
Publisher: Cambridge University Press
Published: 2000-05
Total Pages: 286
ISBN-13: 9780521632744
DOWNLOAD EBOOK →This is a concise 2000 introduction at graduate level to ring theory, module theory and number theory.
Author: Tsit-Yuen Lam
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 577
ISBN-13: 1461205255
DOWNLOAD EBOOK →This new book can be read independently from the first volume and may be used for lecturing, seminar- and self-study, or for general reference. It focuses more on specific topics in order to introduce readers to a wealth of basic and useful ideas without the hindrance of heavy machinery or undue abstractions. User-friendly with its abundance of examples illustrating the theory at virtually every step, the volume contains a large number of carefully chosen exercises to provide newcomers with practice, while offering a rich additional source of information to experts. A direct approach is used in order to present the material in an efficient and economic way, thereby introducing readers to a considerable amount of interesting ring theory without being dragged through endless preparatory material.
Author: T.Y. Lam
Publisher: Springer Science & Business Media
Published: 2009-12-08
Total Pages: 427
ISBN-13: 0387488995
DOWNLOAD EBOOK →This volume offers a compendium of exercises of varying degree of difficulty in the theory of modules and rings. It is the companion volume to GTM 189. All exercises are solved in full detail. Each section begins with an introduction giving the general background and the theoretical basis for the problems that follow.
Author: Paul E. Bland
Publisher: Walter de Gruyter
Published: 2011
Total Pages: 467
ISBN-13: 3110250225
DOWNLOAD EBOOK →This book is an introduction to the theory of rings and modules that goes beyond what one normally obtains in a graduate course in abstract algebra. In addition to the presentation of standard topics in ring and module theory, it also covers category theory, homological algebra and even more specialized topics like injective envelopes and proj
Author: Frank W. Anderson
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 386
ISBN-13: 1461244188
DOWNLOAD EBOOK →This book is intended to provide a reasonably self-contained account of a major portion of the general theory of rings and modules suitable as a text for introductory and more advanced graduate courses. We assume the famil iarity with rings usually acquired in standard undergraduate algebra courses. Our general approach is categorical rather than arithmetical. The continuing theme of the text is the study of the relationship between the one-sided ideal structure that a ring may possess and the behavior of its categories of modules. Following a brief outline of set-theoretic and categorical foundations, the text begins with the basic definitions and properties of rings, modules and homomorphisms and ranges through comprehensive treatments of direct sums, finiteness conditions, the Wedderburn-Artin Theorem, the Jacobson radical, the hom and tensor functions, Morita equivalence and duality, de composition theory of injective and projective modules, and semi perfect and perfect rings. In this second edition we have included a chapter containing many of the classical results on artinian rings that have hdped to form the foundation for much of the contemporary research on the representation theory of artinian rings and finite dimensional algebras. Both to illustrate the text and to extend it we have included a substantial number of exercises covering a wide spectrum of difficulty. There are, of course" many important areas of ring and module theory that the text does not touch upon.
Author: John A. Beachy
Publisher: Cambridge University Press
Published: 1999-04-22
Total Pages: 252
ISBN-13: 9780521644075
DOWNLOAD EBOOK →A first-year graduate text or reference for advanced undergraduates on noncommutative aspects of rings and modules.
Author: Paul M. Cohn
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 234
ISBN-13: 1447104757
DOWNLOAD EBOOK →A clear and structured introduction to the subject. After a chapter on the definition of rings and modules there are brief accounts of Artinian rings, commutative Noetherian rings and ring constructions, such as the direct product, Tensor product and rings of fractions, followed by a description of free rings. Readers are assumed to have a basic understanding of set theory, group theory and vector spaces. Over two hundred carefully selected exercises are included, most with outline solutions.
Author: Toma Albu
Publisher: Springer Science & Business Media
Published: 2011-02-04
Total Pages: 200
ISBN-13: 3034600070
DOWNLOAD EBOOK →This book is a collection of invited papers and articles, many presented at the 2008 International Conference on Ring and Module Theory. The papers explore the latest in various areas of algebra, including ring theory, module theory and commutative algebra.
Author: John Dauns
Publisher: Cambridge University Press
Published: 1994-10-28
Total Pages: 470
ISBN-13: 0521462584
DOWNLOAD EBOOK →This book on modern module and non-commutative ring theory is ideal for beginning graduate students. It starts at the foundations of the subject and progresses rapidly through the basic concepts to help the reader reach current research frontiers. Students will have the chance to develop proofs, solve problems, and to find interesting questions. The first half of the book is concerned with free, projective, and injective modules, tensor algebras, simple modules and primitive rings, the Jacobson radical, and subdirect products. Later in the book, more advanced topics, such as hereditary rings, categories and functors, flat modules, and purity are introduced. These later chapters will also prove a useful reference for researchers in non-commutative ring theory. Enough background material (including detailed proofs) is supplied to give the student a firm grounding in the subject.
