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Localization in Noetherian Rings

A. V. Jategaonkar
Localization in Noetherian Rings by A. V. Jategaonkar PDF

Author : A. V. Jategaonkar
Publisher : Cambridge University Press
Page : 341 pages
File Size : 32,45 MB
Release : 1986-03-13
Category : Mathematics
ISBN : 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.

Noetherian Rings and Their Applications

Lance W. Small
Noetherian Rings and Their Applications by Lance W. Small PDF

Author : Lance W. Small
Publisher : American Mathematical Soc.
Page : 130 pages
File Size : 30,28 MB
Release : 1987
Category : Mathematics
ISBN : 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.

An Introduction to Noncommutative Noetherian Rings

K. R. Goodearl
An Introduction to Noncommutative Noetherian Rings by K. R. Goodearl PDF

Author : K. R. Goodearl
Publisher : Cambridge University Press
Page : 372 pages
File Size : 27,48 MB
Release : 2004-07-12
Category : Mathematics
ISBN : 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.