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Author : Carl Faith
Publisher : Springer Science & Business Media
ISBN 13 : 3642653219
Total Pages : 319 pages
Book Rating : 4.6/5 (426 download)
Download or read book Algebra II Ring Theory written by Carl Faith 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:
Author : Bernard R. McDonald
Publisher :
ISBN 13 :
Total Pages : 332 pages
Book Rating : 4.:/5 (42 download)
Download or read book Ring Theory II written by Bernard R. McDonald and published by . This book was released on 1977 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Paul M. Cohn
Publisher : Springer Science & Business Media
ISBN 13 : 1447104757
Total Pages : 234 pages
Book Rating : 4.4/5 (471 download)
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 : Donald S. Passman
Publisher : American Mathematical Soc.
ISBN 13 : 9780821869383
Total Pages : 324 pages
Book Rating : 4.8/5 (693 download)
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 : Carl Faith
Publisher :
ISBN 13 :
Total Pages : 302 pages
Book Rating : 4.:/5 (65 download)
Download or read book Algebra Ii. Ring Theory written by Carl Faith and published by . This book was released on 1976 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Nathan Jacobson
Publisher : American Mathematical Soc.
ISBN 13 : 0821815024
Total Pages : 160 pages
Book Rating : 4.8/5 (218 download)
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 : B. Stenström
Publisher : Springer Science & Business Media
ISBN 13 : 3642660665
Total Pages : 319 pages
Book Rating : 4.6/5 (426 download)
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 : Irving Kaplansky
Publisher : University of Chicago Press
ISBN 13 : 0226424510
Total Pages : 217 pages
Book Rating : 4.2/5 (264 download)
Download or read book Fields and Rings written by Irving Kaplansky and published by University of Chicago Press. This book was released on 1972 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Author : Carl Faith
Publisher :
ISBN 13 : 9783642653223
Total Pages : 328 pages
Book Rating : 4.6/5 (532 download)
Download or read book Algebra II Ring Theory written by Carl Faith and published by . This book was released on 1976-09-01 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Robert Wisbauer
Publisher : Routledge
ISBN 13 : 1351447343
Total Pages : 425 pages
Book Rating : 4.3/5 (514 download)
Download or read book Foundations of Module and Ring Theory written by Robert Wisbauer and published by Routledge. This book was released on 2018-05-11 with total page 425 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Bernard R. McDonald
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (476 download)
Download or read book Ring Theory II written by Bernard R. McDonald and published by . This book was released on 1977 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Miles Reid
Publisher : Cambridge University Press
ISBN 13 : 9780521458894
Total Pages : 172 pages
Book Rating : 4.4/5 (588 download)
Download or read book Undergraduate Commutative Algebra written by Miles Reid and published by Cambridge University Press. This book was released on 1995-11-30 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: Commutative algebra is at the crossroads of algebra, number theory and algebraic geometry. This textbook is affordable and clearly illustrated, and is intended for advanced undergraduate or beginning graduate students with some previous experience of rings and fields. Alongside standard algebraic notions such as generators of modules and the ascending chain condition, the book develops in detail the geometric view of a commutative ring as the ring of functions on a space. The starting point is the Nullstellensatz, which provides a close link between the geometry of a variety V and the algebra of its coordinate ring A=k[V]; however, many of the geometric ideas arising from varieties apply also to fairly general rings. The final chapter relates the material of the book to more advanced topics in commutative algebra and algebraic geometry. It includes an account of some famous 'pathological' examples of Akizuki and Nagata, and a brief but thought-provoking essay on the changing position of abstract algebra in today's world.
Author : A. Mani
Publisher : Springer
ISBN 13 : 3030011623
Total Pages : 733 pages
Book Rating : 4.0/5 (3 download)
Download or read book Algebraic Methods in General Rough Sets written by A. Mani and published by Springer. This book was released on 2019-01-11 with total page 733 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unique collection of research papers offers a comprehensive and up-to-date guide to algebraic approaches to rough sets and reasoning with vagueness. It bridges important gaps, outlines intriguing future research directions, and connects algebraic approaches to rough sets with those for other forms of approximate reasoning. In addition, the book reworks algebraic approaches to axiomatic granularity. Given its scope, the book offers a valuable resource for researchers and teachers in the areas of rough sets and algebras of rough sets, algebraic logic, non classical logic, fuzzy sets, possibility theory, formal concept analysis, computational learning theory, category theory, and other formal approaches to vagueness and approximate reasoning. Consultants in AI and allied fields will also find the book to be of great practical value.
Author : Paul-Jean Cahen
Publisher : CRC Press
ISBN 13 : 1000946762
Total Pages : 489 pages
Book Rating : 4.0/5 (9 download)
Download or read book Commutative Ring Theory written by Paul-Jean Cahen and published by CRC Press. This book was released on 2023-06-14 with total page 489 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents the proceedings of the Second International Conference on Commutative Ring Theory in Fes, Morocco. The text details developments in commutative algebra, highlighting the theory of rings and ideals. It explores commutative algebra's connections with and applications to topological algebra and algebraic geometry.
Author : Huishi Li
Publisher : World Scientific
ISBN 13 : 9814365149
Total Pages : 295 pages
Book Rating : 4.8/5 (143 download)
Download or read book Grobner Bases in Ring Theory written by Huishi Li and published by World Scientific. This book was released on 2012 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: 1. Preliminaries. 1.1. Presenting algebras by relations. 1.2. S-graded algebras and modules. 1.3. [symbol]-filtered algebras and modules -- 2. The [symbol]-leading homogeneous algebra A[symbol]. 2.1. Recognizing A via G[symbol](A): part 1. 2.2. Recognizing A via G[symbol](A): part 2. 2.3. The [symbol-graded isomorphism A[symbol](A). 2.4. Recognizing A via A[symbol] -- 3. Grobner bases: conception and construction. 3.1. Monomial ordering and admissible system. 3.2. Division algorithm and Grobner basis. 3.3. Grobner bases and normal elements. 3.4. Grobner bases w.r.t. skew multiplicative K-bases. 3.5. Grobner bases in K[symbol] and KQ. 3.6. (De)homogenized Grobner bases. 3.7. dh-closed homogeneous Grobner bases -- 4. Grobner basis theory meets PBW theory. 4.1. [symbol]-standard basis [symbol]-PBW isomorphism. 4.2. Realizing [symbol]-PBW isomorphism by Grobner basis. 4.3. Classical PBW K-bases vs Grobner bases. 4.4. Solvable polynomial algebras revisited -- 5. Using A[symbol] in terms of Grobner bases. 5.1. The working strategy. 5.2. Ufnarovski graph. 5.3. Determination of Gelfand-Kirillov Dimension. 5.4. Recognizing Noetherianity. 5.5. Recognizing (semi- )primeness and PI-property. 5.6. Anick's resolution over monomial algebras. 5.7. Recognizing finiteness of global dimension. 5.8. Determination of Hilbert series -- 6. Recognizing (non- )homogeneous p-Koszulity via A[symbol]. 6.1. (Non- )homogeneous p-Koszul algebras. 6.2. Anick's resolution and homogeneous p-Koszulity. 6.3. Working in terms of Grobner bases -- 7. A study of Rees algebra by Grobner bases. 7.1. Defining [symbol] by [symbol]. 7.2. Defining [symbol] by [symbol]. 7.3. Recognizing structural properties of [symbol] via [symbol]. 7.4. An application to regular central extensions. 7.5. Algebras defined by dh-closed homogeneous Grobner bases -- 8. Looking for more Grobner bases. 8.1. Lifting (finite) Grobner bases from O[symbol]. 8.2. Lifting (finite) Grobner bases from a class of algebras. 8.3. New examples of Grobner basis theory. 8.4. Skew 2-nomial algebras. 8.5. Almost skew 2-nomial algebras
Author : Ring Theory Conference Staff
Publisher :
ISBN 13 : 9780608303277
Total Pages : 315 pages
Book Rating : 4.3/5 (32 download)
Download or read book Ring Theory II written by Ring Theory Conference Staff and published by . This book was released on with total page 315 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 : 4.0/5 (346 download)
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.
