Commutative Ring Theory

This book explores commutative ring theory, an important a foundation for algebraic geometry and complex analytical geometry.

H. Matsumura (Author), Miles Reid (Translated by)

9780521367646, Cambridge University Press

Paperback, published 25 May 1989

336 pages
22.9 x 15.3 x 1.8 cm, 0.45 kg

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

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.

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.

Subject Areas: Algebra [PBF]