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 $H^I_j$(M) are finite for all j < i; (ii) I ⊆ Rad (AnnR($H^I_j$(M))) for all j < i. By Matlis duality we extend some results for the finiteness of associated primes of local cohomology modules $H^I_i$(M).