Noncommutative Noetherian Rings

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Overview

This is an updated 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.

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Editorial Reviews

Booknews
Presents a theory of noncommutative Noetherian rings that complements known results of commutative Neotherian rings and noncommutative Artinian rings. The problems are developed with the technique of localization of a commutative ring at a prime ideal. The key to the theory is Goldie's theorem, which demonstrates that localization is possible at the zero ideal of any Neotherian prime ring. Originally published in 1987, this edition has been corrected with only minor revisions. Annotation c. Book News, Inc., Portland, OR (booknews.com)
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Product Details

Table of Contents

Preface to the Revised Edition
Preface
Notation
Preliminaries 1
Pt. I Basic Theory
Ch. 1 Some Noetherian Rings 11
Ch. 2 Quotient Rings and Goldie's Theorem 41
Ch. 3 Structure of Semiprime Goldie Rings 63
Ch. 4 Semiprime Ideals in Noetherian Rings 97
Ch. 5 Some Dedekind-like Rings 141
Pt. II Dimensions
Ch. 6 Krull Dimension 185
Ch. 7 Global Dimension 245
Ch. 8 Gelfand-Kirillov Dimension 297
Pt. III Extensions
Ch. 9 The Nullstellensatz 341
Ch. 10 Prime Ideals in Extension Rings 365
Ch. 11 Stability 403
Ch. 12 K[subscript 0] and Extension Rings 445
Pt. IV Examples
Ch. 13 Polynomial Identity Rings 477
Ch. 14 Enveloping Algebras of Lie Algebras 525
Ch. 15 Rings of Differential Operators on Algebraic Varieties 565
References 595
Index of Notation 621
Index 625
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