Commutative Ring Theory

by H. Matsumura, Miles Reid

Overview

In addition to being an interesting and profound subject in its own right, commutative ring theory is important as a foundation for algebraic geometry and complex analytical geometry. Matsumura covers the basic material, including dimension theory, depth, Cohen-Macaulay rings, Gorenstein rings, Krull rings and valuation rings. More advanced topics such as Ratliff's theorems on chains of prime ideals are also explored. The work is essentially self-contained, the only prerequisite being a sound knowledge of modern algebra, yet the reader is taken to the frontiers of the subject. Exercises are provided at the end of each section and solutions or hints to some of them are given at the end of the book.

Product Details

ISBN-13:	9780521367646
Publisher:	Cambridge University Press
Publication date:	05/25/1989
Series:	Cambridge Studies in Advanced Mathematics , #8
Edition description:	New Edition
Pages:	336
Product dimensions:	6.02(w) x 9.02(h) x 0.71(d)

Table of Contents

Preface; Introduction; Conventions and terminology; 1. Commutative rings and modules; 2. prime ideals; 3. Properties of extension rings; 4. Valuation rings; 5. Dimension theory; 6. Regular sequences; 7. Regular rings; 8. Flatness revisited; 9. Derivations; 10. I-smoothness; 11. Applications of complete local rings; Appendices; References; Index.

Editorial Reviews

"...an absolutely essential companion to researchers in commutative algebra and an important reference for those in neighboring fields." American Scientist

From the Publisher

Graduate textbook for students in commutative algebra covering dimension theory, depth, Cohen-Macaulay rings, Gorenstein rings, Krull rings, and valuation rings. Exercises. Annotation c. Book News, Inc., Portland, OR (booknews.com)

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