Some Results on Weak Essential Submodules

Abstract

Throughout this paper R represents commutative ring with identity and M is a unitary left R-module. The purpose of this paper is to investigate some new results (up to our knowledge) on the concept of weak essential submodules which introduced by Muna A. Ahmed, where a submodule N of an R-module M is called weak essential, if N ? P ? (0) for each nonzero semiprime submodule P of M. In this paper we rewrite this definition in another formula. Some new definitions are introduced and various properties of weak essential submodules are considered.

Keywords

• "Semiprime submodule, Essential submodules, Weak essential submodules, Weak uniform modules, Fully semi-semiprime modules and Fully essential* modules."