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Author:
Publisher: Academic Press
ISBN: 0080873561
Category : Mathematics
Languages : en
Pages : 317
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Book Description
Multiplicative Theory of Ideals
Author: James W. Brewer
Publisher: Springer Science & Business Media
ISBN: 0387367179
Category : Mathematics
Languages : en
Pages : 437
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Book Description
This volume, a tribute to the work of Robert Gilmer, consists of twenty-four articles authored by his most prominent students and followers. These articles combine surveys of past work by Gilmer and others, recent results which have never before seen print, open problems, and extensive bibliographies. The entire collection provides an in-depth overview of the topics of research in a significant and large area of commutative algebra.
Author:
Publisher: Academic Press
ISBN: 0080873561
Category : Mathematics
Languages : en
Pages : 317
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Book Description
Multiplicative Theory of Ideals
Author: Scott Chapman
Publisher: Springer
ISBN: 9783319388533
Category : Mathematics
Languages : en
Pages : 0
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Book Description
This book consists of both expository and research articles solicited from speakers at the conference entitled "Arithmetic and Ideal Theory of Rings and Semigroups," held September 22–26, 2014 at the University of Graz, Graz, Austria. It reflects recent trends in multiplicative ideal theory and factorization theory, and brings together for the first time in one volume both commutative and non-commutative perspectives on these areas, which have their roots in number theory, commutative algebra, and algebraic geometry. Topics discussed include topological aspects in ring theory, Prüfer domains of integer-valued polynomials and their monadic submonoids, and semigroup algebras. It will be of interest to practitioners of mathematics and computer science, and researchers in multiplicative ideal theory, factorization theory, number theory, and algebraic geometry.
Author: Robert W. Gilmer
Publisher:
ISBN:
Category : Ideals (Algebra)
Languages : en
Pages : 700
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Book Description
Author: Scott Chapman
Publisher: Springer
ISBN: 331938855X
Category : Mathematics
Languages : en
Pages : 414
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Book Description
This book consists of both expository and research articles solicited from speakers at the conference entitled "Arithmetic and Ideal Theory of Rings and Semigroups," held September 22–26, 2014 at the University of Graz, Graz, Austria. It reflects recent trends in multiplicative ideal theory and factorization theory, and brings together for the first time in one volume both commutative and non-commutative perspectives on these areas, which have their roots in number theory, commutative algebra, and algebraic geometry. Topics discussed include topological aspects in ring theory, Prüfer domains of integer-valued polynomials and their monadic submonoids, and semigroup algebras. It will be of interest to practitioners of mathematics and computer science, and researchers in multiplicative ideal theory, factorization theory, number theory, and algebraic geometry.
Author: Marco Fontana
Publisher: CRC Press
ISBN: 9780824798161
Category : Mathematics
Languages : en
Pages : 348
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Book Description
Provides a picture of the research that has occurred and the techniques that have been involved in studying Prufer domains since about 1970. The text covers generating ideals in Prufer domains, particular overrings of Prufer domains, applications of the theory of overrings, generalized dedekind domains, polynomial extensions and quasi-Prufer domains, and more.
Author: Marco Fontana
Publisher: Springer Science & Business Media
ISBN: 144196990X
Category : Mathematics
Languages : en
Pages : 491
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Book Description
Commutative algebra is a rapidly growing subject that is developing in many different directions. This volume presents several of the most recent results from various areas related to both Noetherian and non-Noetherian commutative algebra. This volume contains a collection of invited survey articles by some of the leading experts in the field. The authors of these chapters have been carefully selected for their important contributions to an area of commutative-algebraic research. Some topics presented in the volume include: generalizations of cyclic modules, zero divisor graphs, class semigroups, forcing algebras, syzygy bundles, tight closure, Gorenstein dimensions, tensor products of algebras over fields, as well as many others. This book is intended for researchers and graduate students interested in studying the many topics related to commutative algebra.
Author: Manfred Knebusch
Publisher: Springer
ISBN: 3540456252
Category : Mathematics
Languages : en
Pages : 276
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Book Description
The present book is devoted to a study of relative Prüfer rings and Manis valuations, with an eye to application in real and p-adic geometry. If one wants to expand on the usual algebraic geometry over a non-algebraically closed base field, e.g. a real closed field or p-adically closed field, one typically meets lots of valuation domains. Usually they are not discrete and hence not noetherian. Thus, for a further develomemt of real algebraic and real analytic geometry in particular, and certainly also rigid analytic and p-adic geometry, new chapters of commutative algebra are needed, often of a non-noetherian nature. The present volume presents one such chapter.
Author: J. Alajbegovic
Publisher: Springer Science & Business Media
ISBN: 9401127166
Category : Mathematics
Languages : en
Pages : 339
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Book Description
Various types of approximation theorems are frequently used in general commutative algebra, and they have been found to be useful tools in valuation theory, the theory of Abelian lattice ordered groups, multiplicative ideal theory, etc. Part 1 of this volume is devoted to the investigation of approximation theorems from a classical point of view. The chapters of this part deal with fields and rings, partly ordered groups, and with multirings and d-groups. Part II investigates approximation theorems from a general, categorical point of view. This part is essentially self-contained and requires only a basic knowledge of category theory and first-order logic. For researchers and graduate students of commutative algebra, category theory, as well as applications of logic.
Author: Jesse Elliott
Publisher: Springer Nature
ISBN: 3030244016
Category : Mathematics
Languages : en
Pages : 490
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Book Description
This book presents a systematic exposition of the various applications of closure operations in commutative and noncommutative algebra. In addition to further advancing multiplicative ideal theory, the book opens doors to the various uses of closure operations in the study of rings and modules, with emphasis on commutative rings and ideals. Several examples, counterexamples, and exercises further enrich the discussion and lend additional flexibility to the way in which the book is used, i.e., monograph or textbook for advanced topics courses.
