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Introduction to Ring Theory

2012-12-06 Mathematics
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Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 757/5 ( reviews)

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Book Synopsis Introduction to Ring Theory by : Paul M. Cohn

Download or read book Introduction to Ring Theory written by Paul M. Cohn. This book was released on 2012-12-06. 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.

An Introduction to Rings and Modules

2000-05 Mathematics
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Release : 2000-05
Genre : Mathematics
Kind : eBook
Book Rating : 744/5 ( reviews)

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Book Synopsis An Introduction to Rings and Modules by : A. J. Berrick

Download or read book An Introduction to Rings and Modules written by A. J. Berrick. This book was released on 2000-05. Available in PDF, EPUB and Kindle. Book excerpt: This is a concise 2000 introduction at graduate level to ring theory, module theory and number theory.

Rings of Quotients

2012-12-06 Mathematics
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Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 665/5 ( reviews)

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Book Synopsis Rings of Quotients by : B. Stenström

Download or read book Rings of Quotients written by B. Stenström. This book was released on 2012-12-06. 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).

Commutative Ring Theory

1989-05-25 Mathematics
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Release : 1989-05-25
Genre : Mathematics
Kind : eBook
Book Rating : 646/5 ( reviews)

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Book Synopsis Commutative Ring Theory by : Hideyuki Matsumura

Download or read book Commutative Ring Theory written by Hideyuki Matsumura. This book was released on 1989-05-25. Available in PDF, EPUB and Kindle. Book excerpt: This book explores commutative ring theory, an important a foundation for algebraic geometry and complex analytical geometry.

Applied Discrete Structures

2012-02-25 Applied mathematics
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Release : 2012-02-25
Genre : Applied mathematics
Kind : eBook
Book Rating : 297/5 ( reviews)

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Book Synopsis Applied Discrete Structures by : Ken Levasseur

Download or read book Applied Discrete Structures written by Ken Levasseur. This book was released on 2012-02-25. Available in PDF, EPUB and Kindle. Book excerpt: Applied Discrete Structures, is a two semester undergraduate text in discrete mathematics, focusing on the structural properties of mathematical objects. These include matrices, functions, graphs, trees, lattices and algebraic structures. The algebraic structures that are discussed are monoids, groups, rings, fields and vector spaces. Website: http: //discretemath.org Applied Discrete Structures has been approved by the American Institute of Mathematics as part of their Open Textbook Initiative. For more information on open textbooks, visit http: //www.aimath.org/textbooks/. This version was created using Mathbook XML (https: //mathbook.pugetsound.edu/) Al Doerr is Emeritus Professor of Mathematical Sciences at UMass Lowell. His interests include abstract algebra and discrete mathematics. Ken Levasseur is a Professor of Mathematical Sciences at UMass Lowell. His interests include discrete mathematics and abstract algebra, and their implementation using computer algebra systems.

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