ET-Coessential and ET-Coclosed submodules

Firas sh.  Fandi; Sahira M.  Yaseen

doi:10.24996/ijs.2019.60.12.20

Authors

Firas sh. Fandi Mathematics Department, College of Education for Pure Sciences, University Of Anbar, Ramadi, Iraq
Sahira M. Yaseen Mathematics Department, College of Science University of Baghdad, Baghdad,Iraq

DOI:

https://doi.org/10.24996/ijs.2019.60.12.20

Keywords:

ET-small submodule, ET-coessential submodule, ET- coclosed submodule

Abstract

Let M be an R-module, where R be a commutative;ring with identity. In this paper, we defined a new kind of submodules, namely; ET-coessential and ET-Coclosed submodules of M. Let T be a submodule of M. Let K H M, K is called ET-Coessential of H in M (KâŠ†_ET.ce H), if . A submodule H is called ET- coclosed in M of H has no proper coessential submodule in M, we denote by (KâŠ†_ET.cc H) , that is, KâŠ†_ET.ce H implies that K = H. In our work, we introduce;some properties of ET-coessential and ET-coclosed submodules of M.