The finiteness of co-associated primes of local homology modules

Abstract

Let M be a semi-discrete linearly compact module over a commutative noetherian ring R and i a non-negative integer. We show that the set of co-associated primes of the local homology R-module H_i^I (M) is finite in either of the following cases: (i) The R-modules H_j^I (M) are finite for all j < i; (ii) I ⊆ Rad(Ann_R (H_j^I (M))) for all j < i. By Matlis duality we extend some results for the finiteness of associated primes of local cohomology modules H_Iⁱ (M).