The Theory Of Rings

Author : Nathan Jacobson
Publisher : American Mathematical Soc.
ISBN 13 : 0821815024
Total Pages : 160 pages
Book Rating : 4.21/5 ( download)

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Download or read book The Theory of Rings written by Nathan Jacobson and published by American Mathematical Soc.. This book was released on 1943-12-31 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 M. Cohn
Publisher : Springer Science & Business Media
ISBN 13 : 1447104757
Total Pages : 234 pages
Book Rating : 4.59/5 ( download)

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Download or read book Introduction to Ring Theory written by Paul M. Cohn and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : T.Y. Lam
Publisher : Springer Science & Business Media
ISBN 13 : 1475739877
Total Pages : 299 pages
Book Rating : 4.79/5 ( download)

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Download or read book Exercises in Classical Ring Theory written by T.Y. Lam and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : J.W. Gardner
Publisher : CRC Press
ISBN 13 : 9780203913352
Total Pages : 412 pages
Book Rating : 4.53/5 ( download)

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Download or read book Radical Theory of Rings written by J.W. Gardner and published by CRC Press. This book was released on 2003-11-19 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Donald S. Passman
Publisher : American Mathematical Soc.
ISBN 13 : 9780821869383
Total Pages : 324 pages
Book Rating : 4.88/5 ( download)

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Download or read book A Course in Ring Theory written by Donald S. Passman and published by American Mathematical Soc.. This book was released on 2004-09-28 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : B. Stenström
Publisher : Springer Science & Business Media
ISBN 13 : 3642660665
Total Pages : 319 pages
Book Rating : 4.65/5 ( download)

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Download or read book Rings of Quotients written by B. Stenström and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 319 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of rings of quotients has its origin in the work of (j). Ore and K. Asano on the construction of the total ring of fractions, in the 1930's and 40's. But the subject did not really develop until the end of the 1950's, when a number of important papers appeared (by R. E. Johnson, Y. Utumi, A. W. Goldie, P. Gabriel, J. Lambek, and others). Since then the progress has been rapid, and the subject has by now attained a stage of maturity, where it is possible to make a systematic account of it (which is the purpose of this book). The most immediate example of a ring of quotients is the field of fractions Q of a commutative integral domain A. It may be characterized by the two properties: (i) For every qEQ there exists a non-zero SEA such that qSEA. (ii) Q is the maximal over-ring of A satisfying condition (i). The well-known construction of Q can be immediately extended to the case when A is an arbitrary commutative ring and S is a multiplicatively closed set of non-zero-divisors of A. In that case one defines the ring of fractions Q = A [S-l] as consisting of pairs (a, s) with aEA and SES, with the declaration that (a, s)=(b, t) if there exists UES such that uta = usb. The resulting ring Q satisfies (i), with the extra requirement that SES, and (ii).

Author : C. Nastasescu
Publisher : Springer Science & Business Media
ISBN 13 : 9789027724618
Total Pages : 382 pages
Book Rating : 4.1X/5 ( download)

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Download or read book Dimensions of Ring Theory written by C. Nastasescu and published by Springer Science & Business Media. This book was released on 1987-04-30 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The Scandal of Father 'The Hermit Gad in Crane Feathers' in R. Brown 'The point of a Pin'. van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of s9phistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.

Author : S.K. Jain
Publisher : Springer Science & Business Media
ISBN 13 : 1461219787
Total Pages : 330 pages
Book Rating : 4.81/5 ( download)

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Download or read book Advances in Ring Theory written by S.K. Jain and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : I. N. Herstein
Publisher :
ISBN 13 :
Total Pages : 156 pages
Book Rating : 4.61/5 ( download)

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Download or read book Topics in Ring Theory written by I. N. Herstein and published by . This book was released on 1969 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Neal Henry McCoy
Publisher : Chelsea Publishing Company, Incorporated
ISBN 13 :
Total Pages : 184 pages
Book Rating : 4.23/5 ( download)

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Download or read book The Theory of Rings written by Neal Henry McCoy and published by Chelsea Publishing Company, Incorporated. This book was released on 1973 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: