Rings Of Quotients Of Rings Of Functions

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 : Nathan J. Fine
Publisher :
ISBN 13 : 9783000177651
Total Pages : 72 pages
Book Rating : 4.55/5 ( download)

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Download or read book Rings of quotients of rings of functions written by Nathan J. Fine and published by . This book was released on 2005 with total page 72 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Sergio R. López-Permouth
Publisher : Springer Science & Business Media
ISBN 13 : 3034602863
Total Pages : 345 pages
Book Rating : 4.60/5 ( download)

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Download or read book Advances in Ring Theory written by Sergio R. López-Permouth and published by Springer Science & Business Media. This book was released on 2011-01-28 with total page 345 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume consists of refereed research and expository articles by both plenary and other speakers at the International Conference on Algebra and Applications held at Ohio University in June 2008, to honor S.K. Jain on his 70th birthday. The articles are on a wide variety of areas in classical ring theory and module theory, such as rings satisfying polynomial identities, rings of quotients, group rings, homological algebra, injectivity and its generalizations, etc. Included are also applications of ring theory to problems in coding theory and in linear algebra.

Author : Grigore Calugareanu
Publisher : Springer Science & Business Media
ISBN 13 : 9401590044
Total Pages : 193 pages
Book Rating : 4.44/5 ( download)

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Download or read book Exercises in Basic Ring Theory written by Grigore Calugareanu and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: Each undergraduate course of algebra begins with basic notions and results concerning groups, rings, modules and linear algebra. That is, it begins with simple notions and simple results. Our intention was to provide a collection of exercises which cover only the easy part of ring theory, what we have named the "Basics of Ring Theory". This seems to be the part each student or beginner in ring theory (or even algebra) should know - but surely trying to solve as many of these exercises as possible independently. As difficult (or impossible) as this may seem, we have made every effort to avoid modules, lattices and field extensions in this collection and to remain in the ring area as much as possible. A brief look at the bibliography obviously shows that we don't claim much originality (one could name this the folklore of ring theory) for the statements of the exercises we have chosen (but this was a difficult task: indeed, the 28 titles contain approximatively 15.000 problems and our collection contains only 346). The real value of our book is the part which contains all the solutions of these exercises. We have tried to draw up these solutions as detailed as possible, so that each beginner can progress without skilled help. The book is divided in two parts each consisting of seventeen chapters, the first part containing the exercises and the second part the solutions.

Author : Carl Faith
Publisher : CRC Press
ISBN 13 : 1000657310
Total Pages : 120 pages
Book Rating : 4.19/5 ( download)

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Download or read book Injective Modules and Injective Quotient Rings written by Carl Faith and published by CRC Press. This book was released on 2019-08-21 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt: First published in 1982. These lectures are in two parts. Part I, entitled injective Modules Over Levitzki Rings, studies an injective module E and chain conditions on the set A^(E,R) of right ideals annihilated by subsets of E. Part II is on the subject of (F)PF, or (finitely) pseudo-Frobenius, rings [i.e., all (finitely generated) faithful modules generate the category mod-R of all R-modules]. (The PF rings had been introduced by Azumaya as a generalization of quasi-Frobenius rings, but FPF includes infinite products of Prufer domains, e.g., Z w .)

Author : Leonard Gillman
Publisher : Courier Dover Publications
ISBN 13 : 0486816885
Total Pages : 321 pages
Book Rating : 4.83/5 ( download)

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Download or read book Rings of Continuous Functions written by Leonard Gillman and published by Courier Dover Publications. This book was released on 2018-01-16 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: Designed as a text as well as a treatise, the first systematic account of the theory of rings of continuous functions remains the basic graduate-level book in this area. 1960 edition.

Author : Charles E. Aull
Publisher : CRC Press
ISBN 13 : 1000154203
Total Pages : 342 pages
Book Rating : 4.07/5 ( download)

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Download or read book Rings of Continuous Function written by Charles E. Aull and published by CRC Press. This book was released on 2020-12-18 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains papers on algebra, functional analysis, and general topology, with a strong interaction with set theoretic axioms and involvement with category theory, presented in the special session on Rings of Continuous Functions held in 1982 in Cincinnati, Ohio.

Author : B. Stenström
Publisher : Springer
ISBN 13 : 3540370021
Total Pages : 143 pages
Book Rating : 4.24/5 ( download)

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Download or read book Rings and Modules of Quotients written by B. Stenström and published by Springer. This book was released on 2006-11-15 with total page 143 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Ernst Specker
Publisher : Infinite Study
ISBN 13 :
Total Pages : 22 pages
Book Rating : 4./5 ( download)

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Download or read book The Ring of Polyfunctions written by Ernst Specker and published by Infinite Study. This book was released on with total page 22 pages. Available in PDF, EPUB and Kindle. Book excerpt: We study the ring of polyfunctions over a commutative ring R with unit element. The function S generalizes the number theoretic Smarandache function. For the ring R = Z/nZ we provide a unique representation of polynomials which vanish as a function. Moreover we derive a new formula for the size of the ring of polyfunctions in several variables over Z/nZ.

Author : Craig Huneke
Publisher : Cambridge University Press
ISBN 13 : 0521688604
Total Pages : 446 pages
Book Rating : 4.04/5 ( download)

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Download or read book Integral Closure of Ideals, Rings, and Modules written by Craig Huneke and published by Cambridge University Press. This book was released on 2006-10-12 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ideal for graduate students and researchers, this book presents a unified treatment of the central notions of integral closure.