On Closed-Dual Modules

In this paper, we mainly investigate modules and rings with the property that closed submodules are annihilators, which are called closed-dual modules and closed-dual rings. We give some characterizations of these modules and rings, obtain some equivalent conditions for a matrix ring Mn(R) to be a closed-dual ring, and prove that R is a right non-singular and right extending ring if and only if R is a right closed-dual Baer ring.