R-annihilator-Coessential and R-annihilator-Coclosed Submodules

Omar K.  Ibrahim; Alaa A.  Elewi

doi:10.24996/ijs.2020.61.4.14

Authors

Omar K. Ibrahim Department of Mathematics, College of Science, University of Baghdad, Baghdad, Iraq
Alaa A. Elewi Department of Mathematics, College of Science, University of Baghdad, Baghdad, Iraq

DOI:

https://doi.org/10.24996/ijs.2020.61.4.14

Keywords:

Essential submodules, coclosed submodule, coessential submodule, R-annihilator - coessential, R- annihilator -coclosed

Abstract

Let be a unitary left R-module on associative ring with identity. A submodule of is called -annihilator small if , where is a submodule of , implies that ann( )=0, where ann( ) indicates annihilator of in . In this paper, we introduce the concepts of -annihilator-coessential and - annihilator - coclosed submodules. We give many properties related with these types of submodules.