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London Mathematical Society Student Texts : An Introduction to Noncommutative Noetherian Rings Series Number 61 - K. R. Goodearl

London Mathematical Society Student Texts

An Introduction to Noncommutative Noetherian Rings Series Number 61


Published: 1st July 2004
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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. Various important settings, such as group algebras, Lie algebras, and quantum groups, are sketched at the outset to describe typical problems and provide motivation. The text then develops and illustrates the standard ingredients of the theory: e.g., skew polynomial rings, rings of fractions, bimodules, Krull dimension, linked prime ideals. Recurring emphasis is placed on prime ideals, which play a central role in applications to representation theory. 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.

'... well written and perfectly suits for both students beginning to study Ring theory and established mathematicians that are just interested in learning basics of the theory of Noetherian rings.' Zentralblatt MATH
"Readers of the first edition will notice a number of changes in this edition, including a restrucuring of the topics, many more explicit examples, and an increased emphasis on quantum groups, a subject which has flourished in the decade that has passed since the first edition...This level of explicitness would make large parts of the book accessible even to an undergraduate who has only completed a first course in algebra, although the target audience is primarily at the graduate student level." MAA Reviews, Darren Glass

A few Noetherian rings
Skew polynomial rings
Prime ideals
Semisimple modules, Artinian modules, and torsionfree modules
Injective hulls
Semisimple rings of fractions
Modules over semiprime Goldie rings
Bimodules and affiliated prime ideals
Fully bounded rings
Rings and modules of fractions
Artinian quotient rings
Links between prime ideals
The Artin-Rees property
Rings satisfying the second layer condition
Krull dimension
Numbers of generators of modules
Transcendental division algebras
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780521836876
ISBN-10: 0521836875
Series: London Mathematical Society Student Texts
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 370
Published: 1st July 2004
Publisher: Cambridge University Press
Country of Publication: GB
Dimensions (cm): 22.9 x 15.2  x 2.4
Weight (kg): 0.71
Edition Number: 2
Edition Type: Revised