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9780521367646

Commutative Ring Theory

by
  • ISBN13:

    9780521367646

  • ISBN10:

    0521367646

  • Format: Paperback
  • Copyright: 1989-06-30
  • Publisher: Cambridge University Press

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Summary

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.

Table of Contents

Preface
Introduction
Conventions and terminology
Commutative rings and modules
prime ideals
Properties of extension rings
Valuation rings
Dimension theory
Regular sequences
Regular rings
Flatness revisited
Derivations
I-smoothness
Applications of complete local rings
Appendices
References
Index.
Table of Contents provided by Publisher. All Rights Reserved.

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