On Sm-Modules

Abstract

Let R be a commutative ring with identity, and let M be a unitary R-module. We introduce a concept of sm-module as follows: M is called sm-module if and only if Rann Nis a semimaximal ideal of R, for each maximal submodule N of M. In this paper, some properties and characterizations of sm-modules is given also, various basic results a bout sm-module are considered. Moreover, some relations between sm- modules and other types of modules are considered.