On Finiteness Properties on Associated Primes of Local Cohomology Modules and Ext-Modules

Abstract

Abstract. Let R be a commutative Noetherian (not necessarily local) ring, I an ideal of R and M a finitely generated R-module. In this paper, by computing the local cohomology modules and Ext-modules via the injective resolution of M , we proved that, if for an integer t > 0,for ∀ j ≤ t and ∀ n > 0. This shows that n>0 (Ass R Ext i R (R/I n , M )) ≥k is a finite set for ∀ i ≤ t. Also, we prove that