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Localization in Noetherian Rings

Author: A. V. Jategaonkar

Publisher: Cambridge University Press

Published: 1986-03-13

Total Pages: 341

ISBN-13: 0521317134

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This monograph first published in 1986 is a reasonably self-contained account of a large part of the theory of non-commutative Noetherian rings. The author focuses on two important aspects: localization and the structure of infective modules. The former is presented in the opening chapters after which some new module-theoretic concepts and methods are used to formulate a new view of localization. This view, which is one of the book's highlights, shows that the study of localization is inextricably linked to the study of certain injectives and leads, for the first time, to some genuine applications of localization in the study of Noetherian rings. In the last part Professor Jategaonkar introduces a unified setting for four intensively studied classes of Noetherian rings: HNP rings, PI rings, enveloping algebras of solvable Lie algebras, and group rings of polycyclic groups. Some appendices summarize relevant background information about these four classes.

Book Synopsis Localization in Noetherian Rings by : A. V. Jategaonkar

Download or read book Localization in Noetherian Rings written by A. V. Jategaonkar and published by Cambridge University Press. This book was released on 1986-03-13 with total page 341 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph first published in 1986 is a reasonably self-contained account of a large part of the theory of non-commutative Noetherian rings. The author focuses on two important aspects: localization and the structure of infective modules. The former is presented in the opening chapters after which some new module-theoretic concepts and methods are used to formulate a new view of localization. This view, which is one of the book's highlights, shows that the study of localization is inextricably linked to the study of certain injectives and leads, for the first time, to some genuine applications of localization in the study of Noetherian rings. In the last part Professor Jategaonkar introduces a unified setting for four intensively studied classes of Noetherian rings: HNP rings, PI rings, enveloping algebras of solvable Lie algebras, and group rings of polycyclic groups. Some appendices summarize relevant background information about these four classes.

On universal localization of noncommutative Noetherian rings

Author: Christine M. Leroux

Publisher:

Published: 2013

Total Pages: 0

ISBN-13:

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Book Synopsis On universal localization of noncommutative Noetherian rings by : Christine M. Leroux

Download or read book On universal localization of noncommutative Noetherian rings written by Christine M. Leroux and published by . This book was released on 2013 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Noncommutative Noetherian Rings

Author: John C. McConnell

Publisher: American Mathematical Soc.

Published: 2001

Total Pages: 658

ISBN-13: 0821821695

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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.

Book Synopsis Noncommutative Noetherian Rings by : John C. McConnell

Download or read book Noncommutative Noetherian Rings written by John C. McConnell and published by American Mathematical Soc.. This book was released on 2001 with total page 658 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

An Introduction to Noncommutative Noetherian Rings

Author: K. R. Goodearl

Publisher: Cambridge University Press

Published: 2004-07-12

Total Pages: 372

ISBN-13: 9780521545372

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This introduction to noncommutative noetherian rings is intended to be accessible to anyone with a basic background in abstract algebra. It can be used as a second-year graduate text, or as a self-contained reference. Extensive explanatory discussion is given, and exercises are integrated throughout. This edition incorporates substantial revisions, particularly in the first third of the book, where the presentation has been changed to increase accessibility and topicality. New material includes the basic types of quantum groups, which then serve as test cases for the theory developed.

Book Synopsis An Introduction to Noncommutative Noetherian Rings by : K. R. Goodearl

Download or read book An Introduction to Noncommutative Noetherian Rings written by K. R. Goodearl and published by Cambridge University Press. This book was released on 2004-07-12 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introduction to noncommutative noetherian rings is intended to be accessible to anyone with a basic background in abstract algebra. It can be used as a second-year graduate text, or as a self-contained reference. Extensive explanatory discussion is given, and exercises are integrated throughout. This edition incorporates substantial revisions, particularly in the first third of the book, where the presentation has been changed to increase accessibility and topicality. New material includes the basic types of quantum groups, which then serve as test cases for the theory developed.

An Introduction to Noncommutative Noetherian Rings

Author: K. R. Goodearl

Publisher: Cambridge University Press

Published: 1989

Total Pages: 328

ISBN-13: 9780521369251

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Introduces and applies the standard techniques in the area (ring of fractions, bimodules, Krull dimension, linked prime ideals).

Book Synopsis An Introduction to Noncommutative Noetherian Rings by : K. R. Goodearl

Download or read book An Introduction to Noncommutative Noetherian Rings written by K. R. Goodearl and published by Cambridge University Press. This book was released on 1989 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduces and applies the standard techniques in the area (ring of fractions, bimodules, Krull dimension, linked prime ideals).

Classes of Good Noetherian Rings

Author: Cristodor Ionescu

Publisher: Springer Nature

Published: 2023-03-28

Total Pages: 487

ISBN-13: 303122292X

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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.

Book Synopsis Classes of Good Noetherian Rings by : Cristodor Ionescu

Download or read book Classes of Good Noetherian Rings written by Cristodor Ionescu and published by Springer Nature. This book was released on 2023-03-28 with total page 487 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Algebraic Geometry

Author: Robin Hartshorne

Publisher: Springer Science & Business Media

Published: 2013-06-29

Total Pages: 511

ISBN-13: 1475738498

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An introduction to abstract algebraic geometry, with the only prerequisites being results from commutative algebra, which are stated as needed, and some elementary topology. More than 400 exercises distributed throughout the book offer specific examples as well as more specialised topics not treated in the main text, while three appendices present brief accounts of some areas of current research. This book can thus be used as textbook for an introductory course in algebraic geometry following a basic graduate course in algebra. Robin Hartshorne studied algebraic geometry with Oscar Zariski and David Mumford at Harvard, and with J.-P. Serre and A. Grothendieck in Paris. He is the author of "Residues and Duality", "Foundations of Projective Geometry", "Ample Subvarieties of Algebraic Varieties", and numerous research titles.

Book Synopsis Algebraic Geometry by : Robin Hartshorne

Download or read book Algebraic Geometry written by Robin Hartshorne and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 511 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to abstract algebraic geometry, with the only prerequisites being results from commutative algebra, which are stated as needed, and some elementary topology. More than 400 exercises distributed throughout the book offer specific examples as well as more specialised topics not treated in the main text, while three appendices present brief accounts of some areas of current research. This book can thus be used as textbook for an introductory course in algebraic geometry following a basic graduate course in algebra. Robin Hartshorne studied algebraic geometry with Oscar Zariski and David Mumford at Harvard, and with J.-P. Serre and A. Grothendieck in Paris. He is the author of "Residues and Duality", "Foundations of Projective Geometry", "Ample Subvarieties of Algebraic Varieties", and numerous research titles.

Noetherian Rings and Their Applications

Author: Lance W. Small

Publisher: American Mathematical Soc.

Published: 1987

Total Pages: 130

ISBN-13: 0821815253

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". T. Stafford -- The Goldie rank of a module " . R. Farkas -- Noetherian group rings: An exercise in creating folklore and intuition " . C. Jantzen -- Primitive ideals in the enveloping algebra of a semisimple Lie algebra " . J. Enright -- Representation theory of semisimple Lie algebras " .-E. Björk -- Filtered Noetherian rings " . Rentschler -- Primitive ideals in enveloping algebras.

Book Synopsis Noetherian Rings and Their Applications by : Lance W. Small

Download or read book Noetherian Rings and Their Applications written by Lance W. Small and published by American Mathematical Soc.. This book was released on 1987 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: ". T. Stafford -- The Goldie rank of a module " . R. Farkas -- Noetherian group rings: An exercise in creating folklore and intuition " . C. Jantzen -- Primitive ideals in the enveloping algebra of a semisimple Lie algebra " . J. Enright -- Representation theory of semisimple Lie algebras " .-E. Björk -- Filtered Noetherian rings " . Rentschler -- Primitive ideals in enveloping algebras.

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

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.)

Book Synopsis Representation Type of Commutative Noetherian Rings III: Global Wildness and Tameness by : Lee Klingler

Download or read book Representation Type of Commutative Noetherian Rings III: Global Wildness and Tameness written by Lee Klingler and published by American Mathematical Soc.. This book was released on 2005 with total page 187 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.)

Advances in Rings and Modules

Author: Sergio R. López-Permouth

Publisher: American Mathematical Soc.

Published: 2018-09-06

Total Pages: 283

ISBN-13: 1470435551

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This volume, dedicated to Bruno J. Müller, a renowned algebraist, is a collection of papers that provide a snapshot of the diversity of themes and applications that interest algebraists today. The papers highlight the latest progress in ring and module research and present work done on the frontiers of the topics discussed. In addition, selected expository articles are included to give algebraists and other mathematicians, including graduate students, an accessible introduction to areas that may be outside their own expertise.

Book Synopsis Advances in Rings and Modules by : Sergio R. López-Permouth

Download or read book Advances in Rings and Modules written by Sergio R. López-Permouth and published by American Mathematical Soc.. This book was released on 2018-09-06 with total page 283 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume, dedicated to Bruno J. Müller, a renowned algebraist, is a collection of papers that provide a snapshot of the diversity of themes and applications that interest algebraists today. The papers highlight the latest progress in ring and module research and present work done on the frontiers of the topics discussed. In addition, selected expository articles are included to give algebraists and other mathematicians, including graduate students, an accessible introduction to areas that may be outside their own expertise.