Classes Of Good Noetherian Rings

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Classes Of Good Noetherian Rings

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Author : Cristodor Ionescu
language : en
Publisher: Springer Nature
Release Date : 2023-03-28

Classes Of Good Noetherian Rings written by Cristodor Ionescu and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-03-28 with Mathematics categories.

This monograph provides an exhaustive treatment of several classes of Noetherian rings and morphisms of Noetherian local rings. Chapters carefully examine some of the most important topics in the area, including Nagata, F-finite and excellent rings, Bertini’s Theorem, and Cohen factorizations. Of particular interest is the presentation of Popescu’s Theorem on Neron Desingularization and the structure of regular morphisms, with a complete proof. Classes of Good Noetherian Rings will be an invaluable resource for researchers in commutative algebra, algebraic and arithmetic geometry, and number theory.

Noncommutative Noetherian Rings

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Author : John C. McConnell
language : en
Publisher: American Mathematical Soc.
Release Date : 2001

Noncommutative Noetherian Rings written by John C. McConnell 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 2001 with Mathematics categories.

This is a reprinted edition of a work that was considered the definitive account in the subject area upon its initial publication by J. Wiley & Sons in 1987. It presents, within a wider context, a comprehensive account of noncommutative Noetherian rings. The author covers the major developments from the 1950s, stemming from Goldie's theorem and onward, including applications to group rings, enveloping algebras of Lie algebras, PI rings, differential operators, and localization theory. The book is not restricted to Noetherian rings, but discusses wider classes of rings where the methods apply more generally. In the current edition, some errors were corrected, a number of arguments have been expanded, and the references were brought up to date. This reprinted edition will continue to be a valuable and stimulating work for readers interested in ring theory and its applications to other areas of mathematics.

Interactions Between Ring Theory And Representations Of Algebras

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Author : Freddy Van Oystaeyen
language : en
Publisher: CRC Press
Release Date : 2000-04-05

Interactions Between Ring Theory And Representations Of Algebras written by Freddy Van Oystaeyen and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-04-05 with Mathematics categories.

This work is based on a set of lectures and invited papers presented at a meeting in Murcia, Spain, organized by the European Commission's Training and Mobility of Researchers (TMR) Programme. It contains information on the structure of representation theory of groups and algebras and on general ring theoretic methods related to the theory.

Algebras Rings And Modules

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Author : Michiel Hazewinkel
language : en
Publisher: CRC Press
Release Date : 2016-04-05

Algebras Rings And Modules written by Michiel Hazewinkel and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-04-05 with Mathematics categories.

The theory of algebras, rings, and modules is one of the fundamental domains of modern mathematics. General algebra, more specifically non-commutative algebra, is poised for major advances in the twenty-first century (together with and in interaction with combinatorics), just as topology, analysis, and probability experienced in the twentieth centu

Algebras Rings And Their Representations

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Author : Alberto Facchini
language : en
Publisher: World Scientific
Release Date : 2006

Algebras Rings And Their Representations written by Alberto Facchini and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Mathematics categories.

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. Sample Chapter(s). Chapter 1: Some Coreflective Categories of Topological Modules (221 KB). Contents: Krull Monoids and Their Application in Module Theory (A Facchini); Infinite Progenerator Sums (A Facchini & L S Levy); Quadratic Algebras of Skew Type (E Jespers & J Okn nski); Representation Type of Commutative Noetherian Rings (Introduction) (L Klingler & L S Levy); Corner Ring Theory: A Generalization of Peirce Decompositions (T-Y Lam); Quasideterminants and Right Roots of Polynomials Over Division Rings (B L Osofsky); Injective Dimension Relative to a Torsion Theory (P F Smith); and other papers. Readership: Algebraists, mathematicians interested in the connections between algebra and other fields, and graduate students interested in algebra."

Classes Of Modules

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Author : John Dauns
language : en
Publisher: CRC Press
Release Date : 2006-06-19

Classes Of Modules written by John Dauns and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-06-19 with Mathematics categories.

Because traditional ring theory places restrictive hypotheses on all submodules of a module, its results apply only to small classes of already well understood examples. Often, modules with infinite Goldie dimension have finite-type dimension, making them amenable to use with type dimension, but not Goldie dimension. By working with natural classes

Approximations And Endomorphism Algebras Of Modules

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Author : Rüdiger Göbel
language : en
Publisher: Walter de Gruyter
Release Date : 2012-10-01

Approximations And Endomorphism Algebras Of Modules written by Rüdiger Göbel 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 2012-10-01 with Mathematics categories.

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.

Algebra Ii Ring Theory

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Author : Carl Faith
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Algebra Ii Ring Theory written by Carl Faith 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 2012-12-06 with Mathematics categories.

Model Theory And Modules

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Author : Mike Prest
language : en
Publisher: Cambridge University Press
Release Date : 1988-02-25

Model Theory And Modules written by Mike Prest 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 1988-02-25 with Mathematics categories.

In recent years the interplay between model theory and other branches of mathematics has led to many deep and intriguing results. In this, the first book on the topic, the theme is the interplay between model theory and the theory of modules. The book is intended to be a self-contained introduction to the subject and introduces the requisite model theory and module theory as it is needed. Dr Prest develops the basic ideas concerning what can be said about modules using the information which may be expressed in a first-order language. Later chapters discuss stability-theoretic aspects of modules, and structure and classification theorems over various types of rings and for certain classes of modules. Both algebraists and logicians will enjoy this account of an area in which algebra and model theory interact in a significant way. The book includes numerous examples and exercises and consequently will make an ideal introduction for graduate students coming to this subject for the first time.

Multiplicities And Chern Classes In Local Algebra

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Author : Paul C. Roberts
language : en
Publisher: Cambridge University Press
Release Date : 1998-05-13

Multiplicities And Chern Classes In Local Algebra written by Paul C. Roberts 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 1998-05-13 with Mathematics categories.

Presents the theory of local Chern characters used in commutative algebra in an algebraic setting.