The dual of local cohomology modules

Abstract

Let R be a Noetherian commutative local ring with unity, a be an ideal of R and M be an R-module. Local duality is one way of studying local cohomology modules by obtaining their dual modules. When M is a finitely generated Artinian R-module, so is the ith local cohomology module H_a^i (M ). In this study, we base on the work according to Iyengar, et al., (2007) to obtain conditions for which H _a^i (M ) is the Matlis dual of some R-module N. In addition, we establish conditions for which an R-module T is a Matlis dual of H_a^i (M ) and state conditions when T = N.