A NOTE ON AN R- MODULE WITH APPROXIMATELY-PURE INTERSECTION PROPERTY

Let R be a commutative ring with identity and Let M be left R module. A submodule N of an R- module M is said to be approximately-pure submodule of M (for short AP-pure), if N∩IM ∩ =IN+J(R)M∩(N∩IM), for each ideal top of R. the main purpose of this paper is to develop the properties of modules with the approximately- pure intersection property.