Let
be a commutative Noetherian ring and let
be a
semidualizing
-module. The aim of this paper is to introduce and
study the relative version of Matlis duality with respect to
and
some other related topics. In particular, it is shown that over
local ring
, the relative Matlis dual of a Noetherian
-module
is Artinian, and in the case that
is complete the relative
Matlis dual of an Artinian
-module is Noetherian.