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

i
finite properties of generalized local cohomology modules HI(M,N). Set

r
IM =ann(M/IM)andr=depth(IM,N). WeshowthatAssHI(M,N)=

r
AssExtR(M/IM,N). We also characterize the least integer i such that

i
HI(M,N) is not artinian by using the notion of filter regular sequences.