SERRE SUBCATEGORY, LOCAL HOMOLOGY AND LOCAL COHOMOLOGY

This paper deals with local homology modules and local cohomology modules contained in a Serre subcategory of the category of R-modules. For an ideal a of R, we define the concept of the condition C^a on a Serre category which is dual to the condition Ca of Melkersson. As a main result we show that the local homology module Ha i (M) of a minimax R-module M of any Serre category S satisfying the condition C a belongs to S. Also, if S satisfies the condition C^a, then the local cohomology module Hi a (M) ∈ S for all i ≥ 0.