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Author : B. J. Gardner
Publisher : Longman
Page : 216 pages
File Size : 42,5 Mb
Release : 1989
Category : Associative rings
ISBN : UCSD:31822004184198
Author : Anonim
Publisher : Unknown
Page : 194 pages
File Size : 53,9 Mb
Release : 1989
Category : Electronic
ISBN : OCLC:859793081
Author : R. Wiegandt,J.W. Gardner,Shao-Xue Liu
Publisher : CRC Press
Page : 276 pages
File Size : 54,6 Mb
Release : 1996-04-18
Category : Mathematics
ISBN : 0582292816
First published in 1996. Routledge is an imprint of Taylor & Francis, an informa company.
Author : J.W. Gardner,R. Wiegandt
Publisher : CRC Press
Page : 412 pages
File Size : 43,8 Mb
Release : 2003-11-19
Category : Mathematics
ISBN : 0203913353
Radical Theory of Rings distills the most noteworthy present-day theoretical topics, gives a unified account of the classical structure theorems for rings, and deepens understanding of key aspects of ring theory via ring and radical constructions. Assimilating radical theory's evolution in the decades since the last major work on rings and radicals was published, the authors deal with some distinctive features of the radical theory of nonassociative rings, associative rings with involution, and near-rings. Written in clear algebraic terms by globally acknowledged authorities, the presentation includes more than 500 landmark and up-to-date references providing direction for further research.
Author : Richárd Wiegandt
Publisher : Kingston, Ont. : Queen's University
Page : 258 pages
File Size : 52,8 Mb
Release : 1974
Category : Associative rings
ISBN : UVA:X001320623
Author : Friedrich Kasch,Adolf Mader
Publisher : Springer Science & Business Media
Page : 154 pages
File Size : 47,9 Mb
Release : 2004-06-25
Category : Mathematics
ISBN : 3764371250
Accessible to anyone with a basic knowledge of ring and module theory A short introduction to torsion-free Abelian groups is included
Author : Gregory Karpilovsky
Publisher : Unknown
Page : 592 pages
File Size : 43,7 Mb
Release : 1991
Category : Algebra
ISBN : UOM:39015022060308
This book aims to provide comprehensive coverage of the structure of the Jacobson radical of classical rings. Special attention is drawn to the discoveries concerning the Jacobson radical of graded rings. The main objective has been to present an accessible, self-contained and detailed coverage of the present state of the subject, so that the reader can find in one place all that is needed for a thorough understanding of the main results, along with concrete information on how the ideas are applied.
Author : John Dauns
Publisher : Cambridge University Press
Page : 470 pages
File Size : 42,9 Mb
Release : 1994-10-28
Category : Mathematics
ISBN : 9780521462587
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.
Author : Andor Kertesz
Publisher : Unknown
Page : 520 pages
File Size : 42,6 Mb
Release : 1971
Category : Associative rings
ISBN : OCLC:396756609
Author : Andor Kertész
Publisher : Unknown
Page : 528 pages
File Size : 55,8 Mb
Release : 1973
Category : Mathematics
ISBN : UCAL:B4407362
Author : B. J. Gardner
Publisher : Longman Scientific and Technical
Page : 216 pages
File Size : 45,9 Mb
Release : 1989
Category : Mathematics
ISBN : UOM:39015015337556
Author : Joachim Lambek
Publisher : American Mathematical Soc.
Page : 196 pages
File Size : 53,6 Mb
Release : 2009
Category : Associative rings
ISBN : 9780821849002
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 : Paul E. Bland
Publisher : Walter de Gruyter
Page : 467 pages
File Size : 42,5 Mb
Release : 2011
Category : Mathematics
ISBN : 9783110250220
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 : Michiel Hazewinkel,Nadiya Gubareni,V.V. Kirichenko
Publisher : Springer Science & Business Media
Page : 393 pages
File Size : 40,5 Mb
Release : 2006-01-18
Category : Mathematics
ISBN : 9781402026911
Accosiative rings and algebras are very interesting algebraic structures. In a strict sense, the theory of algebras (in particular, noncommutative algebras) originated fromasingleexample,namelythequaternions,createdbySirWilliamR.Hamilton in1843. Thiswasthe?rstexampleofanoncommutative”numbersystem”. During thenextfortyyearsmathematiciansintroducedotherexamplesofnoncommutative algebras, began to bring some order into them and to single out certain types of algebras for special attention. Thus, low-dimensional algebras, division algebras, and commutative algebras, were classi?ed and characterized. The ?rst complete results in the structure theory of associative algebras over the real and complex ?elds were obtained by T.Molien, E.Cartan and G.Frobenius. Modern ring theory began when J.H.Wedderburn proved his celebrated cl- si?cation theorem for ?nite dimensional semisimple algebras over arbitrary ?elds. Twenty years later, E.Artin proved a structure theorem for rings satisfying both the ascending and descending chain condition which generalized Wedderburn structure theorem. The Wedderburn-Artin theorem has since become a corn- stone of noncommutative ring theory. The purpose of this book is to introduce the subject of the structure theory of associative rings. This book is addressed to a reader who wishes to learn this topic from the beginning to research level. We have tried to write a self-contained book which is intended to be a modern textbook on the structure theory of associative rings and related structures and will be accessible for independent study.
Author : Robert Wisbauer
Publisher : Routledge
Page : 425 pages
File Size : 50,9 Mb
Release : 2018-05-11
Category : Mathematics
ISBN : 9781351447348
This volume provides a comprehensive introduction to module theory and the related part of ring theory, including original results as well as the most recent work. It is a useful and stimulating study for those new to the subject as well as for researchers and serves as a reference volume. Starting form a basic understanding of linear algebra, the theory is presented and accompanied by complete proofs. For a module M, the smallest Grothendieck category containing it is denoted by o[M] and module theory is developed in this category. Developing the techniques in o[M] is no more complicated than in full module categories and the higher generality yields significant advantages: for example, module theory may be developed for rings without units and also for non-associative rings. Numerous exercises are included in this volume to give further insight into the topics covered and to draw attention to related results in the literature.
