Pure–supplemented modules

Abstract EN

Let R be an associative ring with identity and M be unital non zero right Rmodule.

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/P and (A+P)/A « M/A