On the local homology theory for artinian modules

Abstract

Let A be a non-zero Artinian R-module. For an arbitrary ideal I of R, we show that the local homology module Hpx(A) is independent of the choice of x whenever 0:A I = 0:A(x1,..., xr). Thus, identifying these modules, we write HpI(A). In this paper we prove that there is a certain duality between HiI(A) and the local cohomology modules and provide some information about the vanishing local homology module HiI(A) which gives an improved form of the main results of [22].