The Cohen-Macaulay and Gorenstein Rees Algebras Associated to Filtrations
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The Cohen-Macaulay and Gorenstein Rees Algebras Associated to Filtrations 电子书下载

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书名：The Cohen-Macaulay and Gorenstein Rees Algebras Associated to Filtrations

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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.

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Cohen Macaulay Gorenstein Rees Algebras Associated Filtrations

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