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Author: J.W. Gardner
Publisher: CRC Press
ISBN: 9780203913352
Category : Mathematics
Languages : en
Pages : 412
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Book Description
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: J.W. Gardner
Publisher: CRC Press
ISBN: 9780203913352
Category : Mathematics
Languages : en
Pages : 412
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Book Description
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: T.Y. Lam
Publisher: Springer Science & Business Media
ISBN: 1475739877
Category : Mathematics
Languages : en
Pages : 299
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Book Description
Based in large part on the comprehensive "First Course in Ring Theory" by the same author, this book provides a comprehensive set of problems and solutions in ring theory that will serve not only as a teaching aid to instructors using that book, but also for students, who will see how ring theory theorems are applied to solving ring-theoretic problems and how good proofs are written. The author demonstrates that problem-solving is a lively process: in "Comments" following many solutions he discusses what happens if a hypothesis is removed, whether the exercise can be further generalized, what would be a concrete example for the exercise, and so forth. The book is thus much more than a solution manual.
Author: L. Márki
Publisher: Elsevier
ISBN: 148329644X
Category : Mathematics
Languages : en
Pages : 311
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Book Description
Radicals arose originally from structural investigations in rings, but later on they infiltrated into various branches of algebra, as well as into topology and relational structures. This volume is the result of a conference attended by mathematicians from all five continents and thus represents the current state of research in the area.
Author: Nathan Jacobson
Publisher: American Mathematical Soc.
ISBN: 0821815024
Category : Mathematics
Languages : en
Pages : 160
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Book Description
The book is mainly concerned with the theory of rings in which both maximal and minimal conditions hold for ideals (except in the last chapter, where rings of the type of a maximal order in an algebra are considered). The central idea consists of representing rings as rings of endomorphisms of an additive group, which can be achieved by means of the regular representation.
Author: Paul E. Bland
Publisher: Walter de Gruyter
ISBN: 3110250225
Category : Mathematics
Languages : en
Pages : 467
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Book Description
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: T.Y. Lam
Publisher: Springer Science & Business Media
ISBN: 1468404067
Category : Mathematics
Languages : en
Pages : 410
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Book Description
One of my favorite graduate courses at Berkeley is Math 251, a one-semester course in ring theory offered to second-year level graduate students. I taught this course in the Fall of 1983, and more recently in the Spring of 1990, both times focusing on the theory of noncommutative rings. This book is an outgrowth of my lectures in these two courses, and is intended for use by instructors and graduate students in a similar one-semester course in basic ring theory. Ring theory is a subject of central importance in algebra. Historically, some of the major discoveries in ring theory have helped shape the course of development of modern abstract algebra. Today, ring theory is a fer tile meeting ground for group theory (group rings), representation theory (modules), functional analysis (operator algebras), Lie theory (enveloping algebras), algebraic geometry (finitely generated algebras, differential op erators, invariant theory), arithmetic (orders, Brauer groups), universal algebra (varieties of rings), and homological algebra (cohomology of rings, projective modules, Grothendieck and higher K-groups). In view of these basic connections between ring theory and other branches of mathemat ics, it is perhaps no exaggeration to say that a course in ring theory is an indispensable part of the education for any fledgling algebraist. The purpose of my lectures was to give a general introduction to the theory of rings, building on what the students have learned from a stan dard first-year graduate course in abstract algebra.
Author: László Márki
Publisher: Elsevier Science & Technology
ISBN:
Category : Mathematics
Languages : en
Pages : 788
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Book Description
Author: Robert Wisbauer
Publisher: Routledge
ISBN: 1351447343
Category : Mathematics
Languages : en
Pages : 622
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Book Description
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.
Author: Yurj A. Drozd
Publisher: Springer Science & Business Media
ISBN: 3642762441
Category : Mathematics
Languages : en
Pages : 260
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Book Description
This English edition has an additional chapter "Elements of Homological Al gebra". Homological methods appear to be effective in many problems in the theory of algebras; we hope their inclusion makes this book more complete and self-contained as a textbook. We have also taken this occasion to correct several inaccuracies and errors in the original Russian edition. We should like to express our gratitude to V. Dlab who has not only metic ulously translated the text, but has also contributed by writing an Appendix devoted to a new important class of algebras, viz. quasi-hereditary algebras. Finally, we are indebted to the publishers, Springer-Verlag, for enabling this book to reach such a wide audience in the world of mathematical community. Kiev, February 1993 Yu.A. Drozd V.V. Kirichenko Preface The theory of finite dimensional algebras is one of the oldest branches of modern algebra. Its origin is linked to the work of Hamilton who discovered the famous algebra of quaternions, and Cayley who developed matrix theory. Later finite dimensional algebras were studied by a large number of mathematicians including B. Peirce, C.S. Peirce, Clifford, ·Weierstrass, Dedekind, Jordan and Frobenius. At the end of the last century T. Molien and E. Cartan described the semisimple algebras over the complex and real fields and paved the first steps towards the study of non-semi simple algebras.
Author: Irving Kaplansky
Publisher: University of Chicago Press
ISBN: 0226424510
Category : Mathematics
Languages : en
Pages : 217
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Book Description
This book combines in one volume Irving Kaplansky's lecture notes on the theory of fields, ring theory, and homological dimensions of rings and modules. "In all three parts of this book the author lives up to his reputation as a first-rate mathematical stylist. Throughout the work the clarity and precision of the presentation is not only a source of constant pleasure but will enable the neophyte to master the material here presented with dispatch and ease."—A. Rosenberg, Mathematical Reviews
