SOME FINITE PROPERTIES OF GENERALIZED LOCAL COHOMOLOGY MODULES

Abstract

Let (R,m) be a commutative Noetherian local ring,I an ideal of R and M,N finitely generated R−modules. In this paper we prove some finite properties of generalized local cohomology modules Hi I(M,N). Set IM = ann(M/IM) andr = depth( IM,N). We show that AssHr I (M,N)= AssExtr R(M/IM,N). We also characterize the least integer i such that Hi I(M,N) is not artinian by using the notion of filter regular sequences.