Noncommutative Noetherian Rings

Noncommutative Noetherian Rings

by J. C. McConnell, J. C. Robson

Hardcover

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Overview

Provides a comprehensive account of the major developments in this important branch of ring theory which have taken place over the past 30 years. Much of the material which comprises this volume has not appeared anywhere in book form before, and the authors have improved and simplified many of the accounts available in journals. The first few chapters form a ''basic course'' which introduces the reader to the subject. Subsequent chapters are each relatively self-contained, so that readers interested in a particular subject can easily consult the sections they want. Specific topics covered include rings arising from matrices, differential operators, and Lie algebras. Contains extensive references.

Product Details

ISBN-13: 9780471915508
Publisher: Wiley
Publication date: 02/18/1988
Series: Pure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts Series , #1
Pages: 614
Product dimensions: 6.40(w) x 10.88(h) x 1.70(d)

Table of Contents

Preliminaries.

BASIC THEORY.

Some Noetherian Rings.

Quotient Rings and Goldie's Theorem.

Structure of Semiprime Goldie Rings.

Semiprime Ideals in Noetherian Rings.

Some Dedekind-Like Rings.

DIMENSIONS.

Krull Dimension.

Global Dimension.

Gelfand Kirillov Dimension.

EXTENSIONS.

The Nullstellensatz.

Prime Ideals in Extension Rings.

Stability.

Ko and Extension Rings.

EXAMPLES.

Polynomial Identity Rings.

Enveloping Algebras of Lie Algebras.

Rings of Differential Operators on Algebraic Varieties.

References.

Index of Notations.

Index.

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