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Memoirs of the American Mathematical Society
1994; 134 pp; softcover
List Price: US$40
Individual Members: US$24
Institutional Members: US$32
Order Code: MEMO/110/526
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.
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