On Pure Multiplication Modules

Abstract

Let R be a commutative ring with identity and M be a unitary left R-module. A submodule N
of an R-module M is called pure if, IN  N IM for all ideal I of R. In this paper, we shall investigate
and study some various properties of the concept of pure multiplication modules, which is appeared in [3]
as a proper generalization of multiplication modules, where an R-module M is called pure multiplication
if for every pure submodule N of M there exists an ideal I of R such that N  IM . We give a number of
results concerning pure multiplication modules. Also, we discussed some properties of pure submodules
of pure multiplication modules.