Local homology and Serre categories

Abstract

We show some results about local homology modules when they are in a Serre subcategory of the category of R-modules. For an ideal a of R, we also define the concept of the condition C a on a Serre category, which seems dual to the condition Ca in Melkersson [1]. As a main result we show that for an Artinian R-module M and any Serre subcategory S of the category of R-modules and a non-negative integer s, HomR(R/a, H a s (M)) ∈ S if H a i (M) ∈ S for all i > s.