| eBook ISBN: | 978-1-4704-0105-4 |
| Product Code: | MEMO/110/526.E |
| List Price: | $42.00 |
| MAA Member Price: | $37.80 |
| AMS Member Price: | $25.20 |
| eBook ISBN: | 978-1-4704-0105-4 |
| Product Code: | MEMO/110/526.E |
| List Price: | $42.00 |
| MAA Member Price: | $37.80 |
| AMS Member Price: | $25.20 |
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 110; 1994; 134 ppMSC: Primary 13; 14
This monograph consists of two parts. Part I investigates the Cohen-Macaulay and Gorenstein properties of symbolic Rees algebras for one-dimensional prime ideals in Cohen-Macaulay local rings. Practical criteria for these algebras to be Cohen-Macaulay and Gorenstein rings are described in terms of certain elements in the prime ideals. This framework is generalized in Part II to Rees algebras \(R(F)\) and graded rings \(G(F)\) associated to general filtrations of ideals in arbitrary Noetherian local rings. Goto and Nishida give certain cohomological characterizations for algebras \(R(F)\) to be Cohen-Macaulay or Gorenstein rings in connection with the corresponding ring-theoretic properties of \(G(F)\). In this way, readers follow a history of the development of the ring theory of Rees algebras. The book raises many important open questions.
ReadershipCommutative algebraists, algebraic geometers, and specialists working on singularities.
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Table of Contents
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Chapters
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I. The Cohen-Macaulay symbolic Rees algebras for curue singularities
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II. Filtrations and the Gorenstein property of the associated Rees algebras
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This monograph consists of two parts. Part I investigates the Cohen-Macaulay and Gorenstein properties of symbolic Rees algebras for one-dimensional prime ideals in Cohen-Macaulay local rings. Practical criteria for these algebras to be Cohen-Macaulay and Gorenstein rings are described in terms of certain elements in the prime ideals. This framework is generalized in Part II to Rees algebras \(R(F)\) and graded rings \(G(F)\) associated to general filtrations of ideals in arbitrary Noetherian local rings. Goto and Nishida give certain cohomological characterizations for algebras \(R(F)\) to be Cohen-Macaulay or Gorenstein rings in connection with the corresponding ring-theoretic properties of \(G(F)\). In this way, readers follow a history of the development of the ring theory of Rees algebras. The book raises many important open questions.
Commutative algebraists, algebraic geometers, and specialists working on singularities.
-
Chapters
-
I. The Cohen-Macaulay symbolic Rees algebras for curue singularities
-
II. Filtrations and the Gorenstein property of the associated Rees algebras
