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  3. Commutative Ring Theory
  • Cited by 194
Publisher:
Cambridge University Press
Online publication date:
June 2012
Print publication year:
1987
Online ISBN:
9781139171762
DOI:
https://doi.org/10.1017/CBO9781139171762
Subjects:
Mathematics (general), Mathematics, Algebra
Series:
Cambridge Studies in Advanced Mathematics (8)
Information

Book description

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.

Reviews

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

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