ON MODULES WHOSE LOCAL COHOMOLOGY MODULES HAVE GENERALIZED COHEN-MACAULAY MATLIS DUALS

Abstract

We consider the Matlis duals
Ki(M) = HomA(Hi m(M),E(A/m))
of the i-th local cohomology module Hi m(M) ofM with respect to the maximal ideal m and E(A/m) is the injective hull of A/m as a module on the m-adic completion A. In this paper, we study the structure of modules M which are satisfied the condition that, for all i =1,...,d−1, either Ki(M) is a generalized Cohen-Macaulay module of dimension i or (Ki(M)) < ∞. We also present some counterexamples to a conjecture given in [4].