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Author : A. J. Berrick
Publisher : Cambridge University Press
Page : 286 pages
File Size : 25,25 MB
Release : 2000-05
Category : Mathematics
ISBN : 9780521632744
This is a concise 2000 introduction at graduate level to ring theory, module theory and number theory.
Author : C. Musili
Publisher : Alpha Science International, Limited
Page : 192 pages
File Size : 41,37 MB
Release : 1994
Category : Mathematics
ISBN : 9788173190377
This book is a self-contained elementary introduction to rings and modules, and should be useful for courses on Algebra. The emphasis is on concept development with adequate examples and counter-examples drawn from topics such as analysis, topology, etc. The entire material, including exercises, is fully class tested.
Author : Joachim Lambek
Publisher :
Page : 206 pages
File Size : 20,85 MB
Release : 1966
Category : Associative rings
ISBN :
Author : Paul M. Cohn
Publisher : Springer Science & Business Media
Page : 234 pages
File Size : 15,1 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 1447104757
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 : Paul E. Bland
Publisher : Walter de Gruyter
Page : 467 pages
File Size : 33,63 MB
Release : 2011
Category : Mathematics
ISBN : 3110250225
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 : Tsit-Yuen Lam
Publisher : Springer Science & Business Media
Page : 577 pages
File Size : 25,73 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 1461205255
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 : Toma Albu
Publisher : Springer Science & Business Media
Page : 204 pages
File Size : 30,54 MB
Release : 2011-02-04
Category : Mathematics
ISBN : 3034600070
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 : Joachim Lambek
Publisher : American Mathematical Soc.
Page : 196 pages
File Size : 36,16 MB
Release : 2009
Category : Associative rings
ISBN : 082184900X
This book is an introduction to the theory of associative rings and their modules, designed primarily for graduate students. The standard topics on the structure of rings are covered, with a particular emphasis on the concept of the complete ring of quotients. A survey of the fundamental concepts of algebras in the first chapter helps to make the treatment self-contained. The topics covered include selected results on Boolean and other commutative rings, the classical structure theory of associative rings, injective modules, and rings of quotients. The final chapter provides an introduction to homological algebra. Besides three appendices on further results, there is a six-page section of historical comments. Table of Contents: Fundamental Concepts of Algebra: 1.1 Rings and related algebraic systems; 1.2 Subrings, homomorphisms, ideals; 1.3 Modules, direct products, and direct sums; 1.4 Classical isomorphism theorems. Selected Topics on Commutative Rings: 2.1 Prime ideals in commutative rings; 2.2 Prime ideals in special commutative rings; 2.3 The complete ring of quotients of a commutative ring; 2.4 Rings of quotients of commutative semiprime rings; 2.5 Prime ideal spaces.Classical Theory of Associative Rings: 3.1 Primitive rings; 3.2 Radicals; 3.3 Completely reducible modules; 3.4 Completely reducible rings; 3.5 Artinian and Noetherian rings; 3.6 On lifting idempotents; 3.7 Local and semiperfect rings. Injectivity and Related Concepts: 4.1 Projective modules; 4.2 Injective modules; 4.3 The complete ring of quotients; 4.4 Rings of endomorphisms of injective modules; 4.5 Regular rings of quotients; 4.6 Classical rings of quotients; 4.7 The Faith-Utumi theorem. Introduction to Homological Algebra: 5.1 Tensor products of modules; 5.2 Hom and $\otimes$ as functors; 5.3 Exact sequences; 5.4 Flat modules; 5.5 Torsion and extension products. Appendixes; Comments; Bibliography; Index. Review from Zentralblatt Math: Due to their clarity and intelligible presentation, these lectures on rings and modules are a particularly successful introduction to the surrounding circle of ideas. Review from American Mathematical Monthly: An introduction to associative rings and modules which requires of the reader only the mathematical maturity which one would attain in a first-year graduate algebra [course]...in order to make the contents of the book as accessible as possible, the author develops all the fundamentals he will need.In addition to covering the basic topics...the author covers some topics not so readily available to the nonspecialist...the chapters are written to be as independent as possible...[which will be appreciated by] students making their first acquaintance with the subject...one of the most successful features of the book is that it can be read by graduate students with little or no help from a specialist. (CHEL/283.H)
Author : John A. Beachy
Publisher : Cambridge University Press
Page : 252 pages
File Size : 35,2 MB
Release : 1999-04-22
Category : Mathematics
ISBN : 9780521644075
A first-year graduate text or reference for advanced undergraduates on noncommutative aspects of rings and modules.
Author : T.Y. Lam
Publisher : Springer Science & Business Media
Page : 427 pages
File Size : 22,73 MB
Release : 2009-12-08
Category : Mathematics
ISBN : 0387488995
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.