On associated graded rings having almost maximal depth

Abstract

We generalize a recent result of Rossi and Valla, and independently Wang, about the depth of G(m) where m is the maximal ideal of a d-d imensional Cohen-Macaulay local ring R having embedding dimesion The generalization removes the restriction on the embedding dimension and replaces it with the condition that where J is a d-generated minimal reduction of m. The main theorem also applies to m-primary ideals I satisfying , where J is a d-generated reduction of I. An example of such an / in a 5-dimensional regular local ring is included as a nontrivial illustration of tie theorem.

1991 Mathematics Subject Classification:

• Primary 13D40
• Primary 13A30
• Primary 13H10