  Let R be a commutative ring with identity and let M be an R-module. The
purpose of this paper is to introduce and investigate the submodules of an
R-module M which satisfy the dual of Property A, the dual of strong Property A,
and the dual of proper strong Property A. Moreover, a submodule N of M which
satisfy Property SJ (N) and Property IM J (N) will be introduced and
investigated.
