On the Local Cohomology of Matlis Reflexive Modules

Abstract

Let R be a commutative Noetherian complete local ring, I an ideal of R, and M, N Matlis reflexive R-modules such that Supp(N) ⊆ V(I). In this note, among other things, we show that is Matlis reflexive for all i and j when one of the following conditions holds:

1. dim(R/I) = 1;

2. I is a principal ideal;

3. dim(R) ≤ 2.

Keywords:

• Bass numbers
• Local cohomology modules
• Matlis duality functor
• Matlis reflexive modules

2000 Mathematics Subject Classification:

• 13D45
• 13C99
• 13C05
• 13D07

Notes

Communicated by I. Swanson.