The Use Of Ultraproducts In Commutative Algebra
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The Use Of Ultraproducts In Commutative Algebra
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Author : Hans Schoutens
language : en
Publisher: Springer
Release Date : 2010-07-16
The Use Of Ultraproducts In Commutative Algebra written by Hans Schoutens and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-07-16 with Mathematics categories.
In spite of some recent applications of ultraproducts in algebra, they remain largely unknown to commutative algebraists, in part because they do not preserve basic properties such as Noetherianity. This work wants to make a strong case against these prejudices. More precisely, it studies ultraproducts of Noetherian local rings from a purely algebraic perspective, as well as how they can be used to transfer results between the positive and zero characteristics, to derive uniform bounds, to define tight closure in characteristic zero, and to prove asymptotic versions of homological conjectures in mixed characteristic. Some of these results are obtained using variants called chromatic products, which are often even Noetherian. This book, neither assuming nor using any logical formalism, is intended for algebraists and geometers, in the hope of popularizing ultraproducts and their applications in algebra.
The Use Of Ultraproducts In Commutative Algebra
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Author : Hans Schoutens
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-07-31
The Use Of Ultraproducts In Commutative Algebra written by Hans Schoutens and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-07-31 with Mathematics categories.
Exploring ultraproducts of Noetherian local rings from an algebraic perspective, this volume illustrates the many ways they can be used in commutative algebra. The text includes an introduction to tight closure in characteristic zero, a survey of flatness criteria, and more.
Ultraproducts In Commutative Algebra
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Author : James A. Nickerson
language : en
Publisher:
Release Date : 1983
Ultraproducts In Commutative Algebra written by James A. Nickerson and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983 with Commutative algebra categories.
Ideal Theoretic Methods In Commutative Algebra
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Author : Daniel Anderson
language : en
Publisher: CRC Press
Release Date : 2019-05-07
Ideal Theoretic Methods In Commutative Algebra written by Daniel Anderson and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-05-07 with Mathematics categories.
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
Commutative Algebra
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Author : Marco Fontana
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-09-29
Commutative Algebra written by Marco Fontana and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-09-29 with Mathematics categories.
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.
Commutative Algebra And Its Applications
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Author : Marco Fontana
language : en
Publisher: Walter de Gruyter
Release Date : 2009-09-04
Commutative Algebra And Its Applications written by Marco Fontana and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-09-04 with Mathematics categories.
This volume contains selected refereed papers based on lectures presented at the ‘Fifth International Fez Conference on Commutative Algebra and Applications’ that was held in Fez, Morocco in June 2008. The volume represents new trends and areas of classical research within the field, with contributions from many different countries. In addition, the volume has as a special focus the research and influence of Alain Bouvier on commutative algebra over the past thirty years.
Multiplicative Ideal Theory In Commutative Algebra
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Author : James W. Brewer
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-12-15
Multiplicative Ideal Theory In Commutative Algebra written by James W. Brewer and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-12-15 with Mathematics categories.
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.
Ultrafilters Throughout Mathematics
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Author : Isaac Goldbring
language : en
Publisher: American Mathematical Society
Release Date : 2022-06-28
Ultrafilters Throughout Mathematics written by Isaac Goldbring and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-06-28 with Mathematics categories.
Ultrafilters and ultraproducts provide a useful generalization of the ordinary limit processes which have applications to many areas of mathematics. Typically, this topic is presented to students in specialized courses such as logic, functional analysis, or geometric group theory. In this book, the basic facts about ultrafilters and ultraproducts are presented to readers with no prior knowledge of the subject and then these techniques are applied to a wide variety of topics. The first part of the book deals solely with ultrafilters and presents applications to voting theory, combinatorics, and topology, while also dealing also with foundational issues. The second part presents the classical ultraproduct construction and provides applications to algebra, number theory, and nonstandard analysis. The third part discusses a metric generalization of the ultraproduct construction and gives example applications to geometric group theory and functional analysis. The final section returns to more advanced topics of a more foundational nature. The book should be of interest to undergraduates, graduate students, and researchers from all areas of mathematics interested in learning how ultrafilters and ultraproducts can be applied to their specialty.
Steps In Commutative Algebra
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Author : R. Y. Sharp
language : en
Publisher: Cambridge University Press
Release Date : 2000
Steps In Commutative Algebra written by R. Y. Sharp and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
Introductory account of commutative algebra, aimed at students with a background in basic algebra.
Commutative Algebra
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Author : Oscar Zariski
language : en
Publisher:
Release Date : 1975
Commutative Algebra written by Oscar Zariski and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1975 with categories.