Commutative ring theory

Hideyuki Matsumura ; translated by M. Reid

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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[目次]

  • 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.

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この本の情報

書名 Commutative ring theory
著作者等 松村 英之
Matsumura Hideyuki
Reid Miles
Reid M.
書名別名 可換環論
シリーズ名 Cambridge studies in advanced mathematics
出版元 Cambridge University Press
刊行年月 1989, c1986
ページ数 xiii, 320 p.
大きさ 23 cm
ISBN 9780521367646
NCID BA26371952
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言語 英語
原文言語 日本語
出版国 イギリス
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