A Note on an R-Modules with Nearly Pure Intersection Property

Abstract

Let R be a commutative ring with identity and let M be a left R–module. A submoduleN of an R-module M is said to be nearly pure of M (abbreviated by N- pure), if N⋂IM=IN+J(M)⋂(N⋂IM), for each ideal Iof R; where J(M) is the Jacobson radical of M. The main purpose of this paper is to introduce the concept of modules with the Nearly Pure intersection property, andwe show that if M=A⊕B, has the NPIP and f:A→B is an R-homomorphism for any N – pure submodules A and B, then kernel f is N-pure.