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 H-R(I)t(M) <= k for for all i < t, then [GRAPHICS] for for all j <= t and for all n > 0. This shows that U-n>0 (Ass(R)Ext(R)(i)(R/I-n,M))(>= k) is a finite set for for all i <= t. Also, we prove that [GRAPHICS] if x(1), x(2), ..., x(r) is M-sequences in dimension > k and n(1), n(2), ... n(r) are some positive integers. Here, for a subset T of Spec(R), set T->= i = {p epsilon T | dimR/p >= i }.