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Author : Robert W. Gilmer
Publisher : New York : M. Dekker
Page : 632 pages
File Size : 48,8 Mb
Release : 1972
Category : Ideals (Algebra).
ISBN : UCAL:B4407306
Author : Franz Halter-Koch
Publisher : CRC Press
Page : 444 pages
File Size : 45,8 Mb
Release : 1998-04-21
Category : Mathematics
ISBN : 0824701860
"Provides for the first time a concise introduction to general and multiplicative ideal theory, valid for commutative rings and monoids and presented in the language of ideal systems on (commutative) monoids."
Author : James W. Brewer,Sarah Glaz,William Heinzer,Bruce Olberding
Publisher : Springer Science & Business Media
Page : 437 pages
File Size : 43,6 Mb
Release : 2006-12-15
Category : Mathematics
ISBN : 9780387367170
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 : Anonim
Publisher : Academic Press
Page : 297 pages
File Size : 48,5 Mb
Release : 1971-10-11
Category : Mathematics
ISBN : 0080873561
Multiplicative Theory of Ideals
Author : Scott Chapman,Marco Fontana,Alfred Geroldinger,Bruce Olberding
Publisher : Springer
Page : 0 pages
File Size : 43,6 Mb
Release : 2016-07-30
Category : Mathematics
ISBN : 3319388533
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 : Scott Chapman,Marco Fontana,Alfred Geroldinger,Bruce Olberding
Publisher : Springer
Page : 407 pages
File Size : 47,5 Mb
Release : 2016-07-29
Category : Mathematics
ISBN : 9783319388557
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 : Unknown
Page : 700 pages
File Size : 46,6 Mb
Release : 1968
Category : Ideals (Algebra)
ISBN : LCCN:76384764
Author : James W. Brewer,Sarah Glaz,William Heinzer,Bruce Olberding
Publisher : Springer
Page : 0 pages
File Size : 40,8 Mb
Release : 2008-11-01
Category : Mathematics
ISBN : 0387505342
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 : Jesse Elliott
Publisher : Springer Nature
Page : 490 pages
File Size : 40,8 Mb
Release : 2019-11-30
Category : Mathematics
ISBN : 9783030244019
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.
Author : Fanggui Wang,Hwankoo Kim
Publisher : Springer
Page : 699 pages
File Size : 53,9 Mb
Release : 2017-01-06
Category : Mathematics
ISBN : 9789811033377
This book provides an introduction to the basics and recent developments of commutative algebra. A glance at the contents of the first five chapters shows that the topics covered are ones that usually are included in any commutative algebra text. However, the contents of this book differ significantly from most commutative algebra texts: namely, its treatment of the Dedekind–Mertens formula, the (small) finitistic dimension of a ring, Gorenstein rings, valuation overrings and the valuative dimension, and Nagata rings. Going further, Chapter 6 presents w-modules over commutative rings as they can be most commonly used by torsion theory and multiplicative ideal theory. Chapter 7 deals with multiplicative ideal theory over integral domains. Chapter 8 collects various results of the pullbacks, especially Milnor squares and D+M constructions, which are probably the most important example-generating machines. In Chapter 9, coherent rings with finite weak global dimensions are probed, and the local ring of weak global dimension two is elaborated on by combining homological tricks and methods of star operation theory. Chapter 10 is devoted to the Grothendieck group of a commutative ring. In particular, the Bass–Quillen problem is discussed. Finally, Chapter 11 aims to introduce relative homological algebra, especially where the related concepts of integral domains which appear in classical ideal theory are defined and investigated by using the class of Gorenstein projective modules. Each section of the book is followed by a selection of exercises of varying degrees of difficulty. This book will appeal to a wide readership from graduate students to academic researchers who are interested in studying commutative algebra.
Author : Daniel Anderson,Ira J. Patrick
Publisher : CRC Press
Page : 378 pages
File Size : 47,9 Mb
Release : 2001-05-04
Category : Mathematics
ISBN : 082470553X
Includes current work of 38 renowned contributors that details the diversity of thought in the fields of commutative algebra and multiplicative ideal theory. Summarizes recent findings on classes of going-down domains and the going-down property, emphasizing new characterizations and applications, as well as generalizations for commutative rings with zero divisors.
Author : Robert W. Gilmer
Publisher : Unknown
Page : 362 pages
File Size : 49,5 Mb
Release : 1968
Category : Ideals (Algebra)
ISBN : STANFORD:36105033266383
Author : Enrico Carlini,Huy Tài Hà,Brian Harbourne,Adam Van Tuyl
Publisher : Springer Nature
Page : 162 pages
File Size : 41,8 Mb
Release : 2020-05-21
Category : Mathematics
ISBN : 9783030452476
This book discusses regular powers and symbolic powers of ideals from three perspectives– algebra, combinatorics and geometry – and examines the interactions between them. It invites readers to explore the evolution of the set of associated primes of higher and higher powers of an ideal and explains the evolution of ideals associated with combinatorial objects like graphs or hypergraphs in terms of the original combinatorial objects. It also addresses similar questions concerning our understanding of the Castelnuovo-Mumford regularity of powers of combinatorially defined ideals in terms of the associated combinatorial data. From a more geometric point of view, the book considers how the relations between symbolic and regular powers can be interpreted in geometrical terms. Other topics covered include aspects of Waring type problems, symbolic powers of an ideal and their invariants (e.g., the Waldschmidt constant, the resurgence), and the persistence of associated primes.
Author : Daniel Anderson,Ira J. Patrick
Publisher : CRC Press
Page : 378 pages
File Size : 52,8 Mb
Release : 2019-05-07
Category : Mathematics
ISBN : 9780429530449
Includes current work of 38 renowned contributors that details the diversity of thought in the fields of commutative algebra and multiplicative ideal theory. Summarizes recent findings on classes of going-down domains and the going-down property, emphasizing new characterizations and applications, as well as generalizations for commutative rings wi
Author : Paulo Ribenboim
Publisher : Springer Science & Business Media
Page : 676 pages
File Size : 51,5 Mb
Release : 2013-11-11
Category : Mathematics
ISBN : 9780387216904
The exposition of the classical theory of algebraic numbers is clear and thorough, and there is a large number of exercises as well as worked out numerical examples. A careful study of this book will provide a solid background to the learning of more recent topics.
