A Course In Ring Theory
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Author |
: Donald S. Passman |
Publisher |
: American Mathematical Soc. |
Total Pages |
: 324 |
Release |
: 2004-09-28 |
ISBN-10 |
: 0821869388 |
ISBN-13 |
: 9780821869383 |
Rating |
: 4/5 (88 Downloads) |
Synopsis A Course in Ring Theory by : Donald S. Passman
Projective modules: Modules and homomorphisms Projective modules Completely reducible modules Wedderburn rings Artinian rings Hereditary rings Dedekind domains Projective dimension Tensor products Local rings Polynomial rings: Skew polynomial rings Grothendieck groups Graded rings and modules Induced modules Syzygy theorem Patching theorem Serre conjecture Big projectives Generic flatness Nullstellensatz Injective modules: Injective modules Injective dimension Essential extensions Maximal ring of quotients Classical ring of quotients Goldie rings Uniform dimension Uniform injective modules Reduced rank Index
Author |
: Paul M. Cohn |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 234 |
Release |
: 2012-12-06 |
ISBN-10 |
: 9781447104759 |
ISBN-13 |
: 1447104757 |
Rating |
: 4/5 (59 Downloads) |
Synopsis Introduction to Ring Theory by : Paul M. Cohn
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 |
: Donald S. Passman |
Publisher |
: American Mathematical Soc. |
Total Pages |
: 322 |
Release |
: 2004 |
ISBN-10 |
: 9780821836804 |
ISBN-13 |
: 0821836803 |
Rating |
: 4/5 (04 Downloads) |
Synopsis A Course in Ring Theory by : Donald S. Passman
A textbook presenting a module theoretic approach to various aspects of commutative and noncommutative ring theory, for students familiar with basic ring theory concepts such as ideals and homomorphisms, but not necessarily with modules. Annotation copyrighted by Book News, Inc., Portland, OR
Author |
: T.Y. Lam |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 410 |
Release |
: 2012-12-06 |
ISBN-10 |
: 9781468404067 |
ISBN-13 |
: 1468404067 |
Rating |
: 4/5 (67 Downloads) |
Synopsis A First Course in Noncommutative Rings by : T.Y. Lam
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 |
: I. N. Herstein |
Publisher |
: |
Total Pages |
: 156 |
Release |
: 1969 |
ISBN-10 |
: UOM:39015017315261 |
ISBN-13 |
: |
Rating |
: 4/5 (61 Downloads) |
Synopsis Topics in Ring Theory by : I. N. Herstein
Author |
: T.Y. Lam |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 299 |
Release |
: 2013-06-29 |
ISBN-10 |
: 9781475739879 |
ISBN-13 |
: 1475739877 |
Rating |
: 4/5 (79 Downloads) |
Synopsis Exercises in Classical Ring Theory by : T.Y. Lam
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 |
: David M. Burton |
Publisher |
: Addison-Wesley |
Total Pages |
: 328 |
Release |
: 1970 |
ISBN-10 |
: UOM:39015015612156 |
ISBN-13 |
: |
Rating |
: 4/5 (56 Downloads) |
Synopsis A First Course in Rings and Ideals by : David M. Burton
Author |
: Toma Albu |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 204 |
Release |
: 2011-02-04 |
ISBN-10 |
: 9783034600071 |
ISBN-13 |
: 3034600070 |
Rating |
: 4/5 (71 Downloads) |
Synopsis Ring and Module Theory by : Toma Albu
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 |
: Tsit-Yuen Lam |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 577 |
Release |
: 2012-12-06 |
ISBN-10 |
: 9781461205258 |
ISBN-13 |
: 1461205255 |
Rating |
: 4/5 (58 Downloads) |
Synopsis Lectures on Modules and Rings by : Tsit-Yuen Lam
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 |
: Nathan Jacobson |
Publisher |
: American Mathematical Soc. |
Total Pages |
: 160 |
Release |
: 1943-12-31 |
ISBN-10 |
: 9780821815021 |
ISBN-13 |
: 0821815024 |
Rating |
: 4/5 (21 Downloads) |
Synopsis The Theory of Rings by : Nathan Jacobson
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.