Let
![$R$](img26.png)
be a commutative Noetherian ring and let
![$C$](img27.png)
be a
semidualizing
![$R$](img26.png)
-module. The aim of this paper is to introduce and
study the relative version of Matlis duality with respect to
![$C$](img27.png)
and
some other related topics. In particular, it is shown that over
local ring
![$R$](img26.png)
, the relative Matlis dual of a Noetherian
![$R$](img26.png)
-module
is Artinian, and in the case that
![$R$](img26.png)
is complete the relative
Matlis dual of an Artinian
![$R$](img26.png)
-module is Noetherian.