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Commutative Ring Theory

Commutative Ring Theory

£54.99

Part of Cambridge Studies in Advanced Mathematics

  • Date Published: May 1989
  • availability: Available
  • format: Paperback
  • isbn: 9780521367646

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  • 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.

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    Product details

    • Date Published: May 1989
    • format: Paperback
    • isbn: 9780521367646
    • length: 336 pages
    • dimensions: 229 x 153 x 18 mm
    • weight: 0.45kg
    • availability: Available
  • 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.

  • Author

    H. Matsumura

    Translator

    Miles Reid

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