PURE – SUPPLEMENTED MODULES

Abstract

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
P
A + P
<<
P
M
and
A
A + P
<<