179 | Mathematics التطبيقية و الصرفةϡوϠعϠ لϡ الھيث إبنةϠ مجدϠ المج28 العدد) 1 ϡ عا( 2015 Ibn Al-Haitham J. for Pure & Appl. Sci. Vol. 28 (1) 2015 On Semi-Essential Submodules Muna A. Ahmed math.200600986@yahoo.com Maysaa R. Abbas maysaa.alsaher@yahoo.comDepartment of Mathematics, college of Science for Women,University of Baghdad, Iraq-Baghdad. Received in : 20 October 2014 , Accepted in :5 January 2015 Abstract Let R be a commutative ring with identity and let M be a unitary left R-module. The purpose of this paper is to investigate some new results (up to our knowledge) on the concept of semi-essential submodules which introduced by Ali S. Mijbass and Nada K. Abdullah, and we make simple changes to the definition relate with the zero submodule, so we say that a submodule N of an R-module M is called semi-essential, if whenever N ∩ P = (0), then P = (0) for each prime submodule P of M. Various properties of semi-essential submodules are considered. Keywords: Essential submodules, Semi-essential submodules, Uniform modules, Semi- uniform modules, Fully prime modules and Fully essential modules. his paper is a part of a thesis submitted by the second author and supervised by the first