Representation Type of Commutative Noetherian Rings III

Representation Type of Commutative Noetherian Rings III PDF

Author: Lee Klingler

Publisher: American Mathematical Soc.

Published: 2005

Total Pages: 170

ISBN-13: 9781470404338

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This memoir completes the series of papers beginning with [KL1,KL2], showing that, for a commutative noetherian ring $\Lambda$, either the category of $\Lambda$-modules of finite length has wild representation type or else we can describe the category of finitely generated $\Lambda$-modules, including their direct-sum relations and local-global relations. (There is a possible exception to our results, involving characteristic 2.)

Representation Type of Commutative Noetherian Rings III: Global Wildness and Tameness

Representation Type of Commutative Noetherian Rings III: Global Wildness and Tameness PDF

Author: Lee Klingler

Publisher: American Mathematical Soc.

Published: 2005

Total Pages: 187

ISBN-13: 0821837389

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This memoir completes the series of papers beginning with [KL1,KL2], showing that, for a commutative noetherian ring $\Lambda$, either the category of $\Lambda$-modules of finite length has wild representation type or else we can describe the category of finitely generated $\Lambda$-modules, including their direct-sum relations and local-global relations. (There is a possible exception to our results, involving characteristic 2.)

Algebras, Rings And Their Representations - Proceedings Of The International Conference On Algebras, Modules And Rings

Algebras, Rings And Their Representations - Proceedings Of The International Conference On Algebras, Modules And Rings PDF

Author: Alberto Facchini

Publisher: World Scientific

Published: 2006-02-20

Total Pages: 403

ISBN-13: 9814478970

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Surveying the most influential developments in the field, this proceedings reviews the latest research on algebras and their representations, commutative and non-commutative rings, modules, conformal algebras, and torsion theories.The volume collects stimulating discussions from world-renowned names including Tsit-Yuen Lam, Larry Levy, Barbara Osofsky, and Patrick Smith.

Abelian Groups, Rings, Modules, and Homological Algebra

Abelian Groups, Rings, Modules, and Homological Algebra PDF

Author: Pat Goeters

Publisher: CRC Press

Published: 2016-04-19

Total Pages: 354

ISBN-13: 142001076X

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About the book In honor of Edgar Enochs and his venerable contributions to a broad range of topics in Algebra, top researchers from around the world gathered at Auburn University to report on their latest work and exchange ideas on some of today's foremost research topics. This carefully edited volume presents the refereed papers of the par

Multiplicative Ideal Theory in Commutative Algebra

Multiplicative Ideal Theory in Commutative Algebra PDF

Author: James W. Brewer

Publisher: Springer Science & Business Media

Published: 2006-12-15

Total Pages: 437

ISBN-13: 0387367179

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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.

Commutative Algebra

Commutative Algebra PDF

Author: Marco Fontana

Publisher: Springer Science & Business Media

Published: 2010-09-29

Total Pages: 491

ISBN-13: 144196990X

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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.

Invariant Means and Finite Representation Theory of $C^*$-Algebras

Invariant Means and Finite Representation Theory of $C^*$-Algebras PDF

Author: Nathanial Patrick Brown

Publisher: American Mathematical Soc.

Published: 2006

Total Pages: 122

ISBN-13: 0821839160

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Various subsets of the tracial state space of a unital C$*$-algebra are studied. The largest of these subsets has a natural interpretation as the space of invariant means. II$ 1$-factor representations of a class of C$*$-algebras considered by Sorin Popa are also studied. These algebras are shown to have an unexpected variety of II$ 1$-factor representations. In addition to developing some general theory we also show that these ideas are related to numerous other problems inoperator algebras.

Approximations and Endomorphism Algebras of Modules

Approximations and Endomorphism Algebras of Modules PDF

Author: Rüdiger Göbel

Publisher: Walter de Gruyter

Published: 2012-10-01

Total Pages: 1002

ISBN-13: 3110218119

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This second, revised and substantially extended edition of Approximations and Endomorphism Algebras of Modules reflects both the depth and the width of recent developments in the area since the first edition appeared in 2006. The new division of the monograph into two volumes roughly corresponds to its two central topics, approximation theory (Volume 1) and realization theorems for modules (Volume 2). It is a widely accepted fact that the category of all modules over a general associative ring is too complex to admit classification. Unless the ring is of finite representation type we must limit attempts at classification to some restricted subcategories of modules. The wild character of the category of all modules, or of one of its subcategories C, is often indicated by the presence of a realization theorem, that is, by the fact that any reasonable algebra is isomorphic to the endomorphism algebra of a module from C. This results in the existence of pathological direct sum decompositions, and these are generally viewed as obstacles to classification. In order to overcome this problem, the approximation theory of modules has been developed. The idea here is to select suitable subcategories C whose modules can be classified, and then to approximate arbitrary modules by those from C. These approximations are neither unique nor functorial in general, but there is a rich supply available appropriate to the requirements of various particular applications. The authors bring the two theories together. The first volume, Approximations, sets the scene in Part I by introducing the main classes of modules relevant here: the S-complete, pure-injective, Mittag-Leffler, and slender modules. Parts II and III of the first volume develop the key methods of approximation theory. Some of the recent applications to the structure of modules are also presented here, notably for tilting, cotilting, Baer, and Mittag-Leffler modules. In the second volume, Predictions, further basic instruments are introduced: the prediction principles, and their applications to proving realization theorems. Moreover, tools are developed there for answering problems motivated in algebraic topology. The authors concentrate on the impossibility of classification for modules over general rings. The wild character of many categories C of modules is documented here by the realization theorems that represent critical R-algebras over commutative rings R as endomorphism algebras of modules from C. The monograph starts from basic facts and gradually develops the theory towards its present frontiers. It is suitable both for graduate students interested in algebra and for experts in module and representation theory.

Asymptotic Behaviour of Tame Harmonic Bundles and an Application to Pure Twistor $D$-Modules, Part 2

Asymptotic Behaviour of Tame Harmonic Bundles and an Application to Pure Twistor $D$-Modules, Part 2 PDF

Author: Takuro Mochizuki

Publisher: American Mathematical Soc.

Published: 2007

Total Pages: 262

ISBN-13: 0821839438

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The author studies the asymptotic behaviour of tame harmonic bundles. First he proves a local freeness of the prolongment of deformed holomorphic bundle by an increasing order. Then he obtains the polarized mixed twistor structure from the data on the divisors. As one of the applications, he obtains the norm estimate of holomorphic or flat sections by weight filtrations of the monodromies. As another application, the author establishes the correspondence of semisimple regularholonomic $D$-modules and polarizable pure imaginary pure twistor $D$-modules through tame pure imaginary harmonic bundles, which is a conjecture of C. Sabbah. Then the regular holonomic version of M. Kashiwara's conjecture follows from the results of Sabbah and the author.

Asymptotic Behaviour of Tame Harmonic Bundles and an Application to Pure Twistor $D$-Modules, Part 1

Asymptotic Behaviour of Tame Harmonic Bundles and an Application to Pure Twistor $D$-Modules, Part 1 PDF

Author: Takuro Mochizuki

Publisher: American Mathematical Soc.

Published: 2007

Total Pages: 344

ISBN-13: 082183942X

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The author studies the asymptotic behaviour of tame harmonic bundles. First he proves a local freeness of the prolongment of deformed holomorphic bundle by an increasing order. Then he obtains the polarized mixed twistor structure from the data on the divisors. As one of the applications, he obtains the norm estimate of holomorphic or flat sections by weight filtrations of the monodromies. As another application, the author establishes the correspondence of semisimple regular holonomic $D$-modules and polarizable pure imaginary pure twistor $D$-modules through tame pure imaginary harmonic bundles, which is a conjecture of C. Sabbah. Then the regular holonomic version of M. Kashiwara's conjecture follows from the results of Sabbah and the author.