On Nearly Prime Submodules of Unitary Modules

Abstract

The aim of this paper is to introduce the notion of nearly prime submodules as a generalization of prime submodules. We investigate some of their basic properties and point out the similarities between these submodules and the prime submodules. We also indicate some applications of nearly prime submodules. These applications show how nearly prime submodules control the structure of modules and they recover earlier relative theorems.