PURE – SUPPLEMENTED MODULES

Let R be an associative ring with identity and M be unital non zero right R- module . M is called H– supplemented module if given any submodule A of M there exist a direct summend submodule D of M such that M = A+X iff M= D+X where X is a submodule of M. In this paper we will give a generalization for H– supplemented which is called pure– supplemented module. An R- module M is called pure– supplemented module if given any submodule A of M there exists a pure submodule P of M such that M = A+X iff M= P+X .Equivalently , for every submodule A of M there exist a pure submodule P of M such that A+P/P M/Pand A+P/A M/A.