Memoirs of the American Mathematical Society 1994; 134 pp; softcover Volume: 110 ISBN10: 0821825844 ISBN13: 9780821825846 List Price: US$42 Individual Members: US$25.20 Institutional Members: US$33.60 Order Code: MEMO/110/526
 This monograph consists of two parts. Part I investigates the CohenMacaulay and Gorenstein properties of symbolic Rees algebras for onedimensional prime ideals in CohenMacaulay local rings. Practical criteria for these algebras to be CohenMacaulay 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 CohenMacaulay or Gorenstein rings in connection with the corresponding ringtheoretic 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. Readership Commutative algebraists, algebraic geometers, and specialists working on singularities. Table of Contents Part I. The CohenMacaulay symbolic Rees algebras for curve singularities  Introduction
 Preliminaries
 The case of dimension 1
 The case of dimension 2
 The CohenMacaulay and Gorenstein properties of \(G_s(\mathbf p)\)
 The CohenMacaulay and Gorenstein properties of \(R_s(\mathbf p)\)
 Examples
 References
Part II. Filtrations and the Gorenstein property of the associated Rees algebras  Introduction
 Preliminaries
 Proof of Theorem (1.1)
 Proof of Theorems (1.3) and (1.5)
 The Gorenstein property of Rees algebras \(R(F)\) and the condition \((S_2)\) for \(A\)
 Graded rings \(R^{\dagger }\)
 Examples for \(R_s(\mathbf p)\)
 Normalized Rees algebras \(\overline R(I)\)
 Bad example
 References
