Item Successfully Added to Cart
An error was encountered while trying to add the item to the cart. Please try again.
OK
Please make all selections above before adding to cart
OK
Share this page via the icons above, or by copying the link below:
Copy To Clipboard
Successfully Copied!
The Cohen-Macaulay and Gorenstein Rees Algebras Associated to Filtrations
 
The Cohen-Macaulay and Gorenstein Rees Algebras Associated to Filtrations
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
The Cohen-Macaulay and Gorenstein Rees Algebras Associated to Filtrations
Click above image for expanded view
The Cohen-Macaulay and Gorenstein Rees Algebras Associated to Filtrations
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
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 1101994; 134 pp
    MSC: 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.

    Readership

    Commutative algebraists, algebraic geometers, and specialists working on singularities.

  • Table of Contents
     
     
    • Chapters
    • I. The Cohen-Macaulay symbolic Rees algebras for curue singularities
    • II. Filtrations and the Gorenstein property of the associated Rees algebras
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 1101994; 134 pp
MSC: 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.

Readership

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
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.