Tight Closure And Its Applications

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Tight Closure And Its Applications

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Author : Craig Huneke
language : en
Publisher: American Mathematical Soc.
Release Date :

Tight Closure And Its Applications written by Craig Huneke and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.

This monograph deals with the theory of tight closure and its applications. The contents are based on ten talks given at a CBMS conference held at North Dakota State University in June 1995.

Tight Closure And Its Applications

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Author : Craig Huneke
language : en
Publisher: American Mathematical Soc.
Release Date : 1996

Tight Closure And Its Applications written by Craig Huneke and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Mathematics categories.

This monograph deals with the theory of tight closure and its applications. The contents are based on ten talks given at a CBMS conference held at North Dakota State University in June 1995.

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.

Progress In Commutative Algebra 2

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Author : Christopher Francisco
language : en
Publisher: Walter de Gruyter
Release Date : 2012-04-26

Progress In Commutative Algebra 2 written by Christopher Francisco 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 2012-04-26 with Mathematics categories.

This is the second of two volumes of a state-of-the-art survey article collection which originates from three commutative algebra sessions at the 2009 Fall Southeastern American Mathematical Society Meeting at Florida Atlantic University. The articles reach into diverse areas of commutative algebra and build a bridge between Noetherian and non-Noetherian commutative algebra. These volumes present current trends in two of the most active areas of commutative algebra: non-noetherian rings (factorization, ideal theory, integrality), and noetherian rings (the local theory, graded situation, and interactions with combinatorics and geometry). This volume contains surveys on aspects of closure operations, finiteness conditions and factorization. Closure operations on ideals and modules are a bridge between noetherian and nonnoetherian commutative algebra. It contains a nice guide to closure operations by Epstein, but also contains an article on test ideals by Schwede and Tucker and one by Enescu which discusses the action of the Frobenius on finite dimensional vector spaces both of which are related to tight closure. Finiteness properties of rings and modules or the lack of them come up in all aspects of commutative algebra. However, in the study of non-noetherian rings it is much easier to find a ring having a finite number of prime ideals. The editors have included papers by Boynton and Sather-Wagstaff and by Watkins that discuss the relationship of rings with finite Krull dimension and their finite extensions. Finiteness properties in commutative group rings are discussed in Glaz and Schwarz's paper. And Olberding's selection presents us with constructions that produce rings whose integral closure in their field of fractions is not finitely generated. The final three papers in this volume investigate factorization in a broad sense. The first paper by Celikbas and Eubanks-Turner discusses the partially ordered set of prime ideals of the projective line over the integers. The editors have also included a paper on zero divisor graphs by Coykendall, Sather-Wagstaff, Sheppardson and Spiroff. The final paper, by Chapman and Krause, concerns non-unique factorization.

Commutative Algebra And Noncommutative Algebraic Geometry

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Author : David Eisenbud
language : en
Publisher: Cambridge University Press
Release Date : 2015-11-19

Commutative Algebra And Noncommutative Algebraic Geometry written by David Eisenbud 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 2015-11-19 with Mathematics categories.

This book surveys fundamental current topics in these two areas of research, emphasising the lively interaction between them. Volume 1 contains expository papers ideal for those entering the field.

Three Lectures On Commutative Algebra

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Author : Holger Brenner
language : en
Publisher: American Mathematical Soc.
Release Date : 2008

Three Lectures On Commutative Algebra written by Holger Brenner and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.

These lectures provides detailed introductions to some of the latest advances in three significant areas of rapid development in commutative algebra and its applications: tight closure and vector bundles; combinatorics and commutative algebra; constructive desingularization."

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.

Homological And Computational Methods In Commutative Algebra

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Author : Aldo Conca
language : en
Publisher: Springer
Release Date : 2017-11-16

Homological And Computational Methods In Commutative Algebra written by Aldo Conca and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-16 with Mathematics categories.

This volume collects contributions by leading experts in the area of commutative algebra related to the INdAM meeting “Homological and Computational Methods in Commutative Algebra” held in Cortona (Italy) from May 30 to June 3, 2016 . The conference and this volume are dedicated to Winfried Bruns on the occasion of his 70th birthday. In particular, the topics of this book strongly reflect the variety of Winfried Bruns’ research interests and his great impact on commutative algebra as well as its applications to related fields. The authors discuss recent and relevant developments in algebraic geometry, commutative algebra, computational algebra, discrete geometry and homological algebra. The book offers a unique resource, both for young and more experienced researchers seeking comprehensive overviews and extensive bibliographic references.

Geometric And Combinatorial Aspects Of Commutative Algebra

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Author : Jurgen Herzog
language : en
Publisher: CRC Press
Release Date : 2001-03-06

Geometric And Combinatorial Aspects Of Commutative Algebra written by Jurgen Herzog and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-03-06 with Mathematics categories.

This work is based on the lectures presented at the International Conference of Commutative Algebra and Algebraic Geometry held in Messina, Italy. It discusses developments and advances in commutative algebra, algebraic geometry, and combinatorics - highlighting the theory of projective schemes, the geometry of curves, determinantal and stable idea

Six Lectures On Commutative Algebra

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Author : J. Elias
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-03-17

Six Lectures On Commutative Algebra written by J. Elias 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 2010-03-17 with Mathematics categories.

Interest in commutative algebra has surged over the past decades. In order to survey and highlight recent developments in this rapidly expanding field, the Centre de Recerca Matematica in Bellaterra organized a ten-days Summer School on Commutative Algebra in 1996. Lectures were presented by six high-level specialists, L. Avramov (Purdue), M.K. Green (UCLA), C. Huneke (Purdue), P. Schenzel (Halle), G. Valla (Genova) and W.V. Vasconcelos (Rutgers), providing a fresh and extensive account of the results, techniques and problems of some of the most active areas of research. The present volume is a synthesis of the lectures given by these authors. Research workers as well as graduate students in commutative algebra and nearby areas will find a useful overview of the field and recent developments in it. Reviews "All six articles are at a very high level; they provide a thorough survey of results and methods in their subject areas, illustrated with algebraic or geometric examples." - Acta Scientiarum Mathematicarum Avramov lecture: "... it contains all the major results [on infinite free resolutions], it explains carefully all the different techniques that apply, it provides complete proofs (...). This will be extremely helpful for the novice as well as the experienced." - Mathematical reviews Huneke lecture: "The topic is tight closure, a theory developed by M. Hochster and the author which has in a short time proved to be a useful and powerful tool. (...) The paper is extremely well organized, written, and motivated." - Zentralblatt MATH Schenzel lecture: "... this paper is an excellent introduction to applications of local cohomology." - Zentralblatt MATH Valla lecture: "... since he is an acknowledged expert on Hilbert functions and since his interest has been so broad, he has done a superb job in giving the readers a lively picture of the theory." - Mathematical reviews Vasconcelos lecture: "This is a very useful survey on invariants of modules over noetherian rings, relations between them, and how to compute them." - Zentralblatt MATH