ON FINITENESS PROPERTIES ON ASSOCIATED PRIMES OF LOCAL COHOMOLOGY MODULES AND EXT-MODULES

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, dim for for and >0. This shows that> is a finite set for . Also, we prove that if is M-sequences in dimension > k and are some positive integers. Here, for a subset T of Spec(R), set .