An Approach to Generalized Extending Modules Via Ec-Closed Submodules

Enas Mustafa Kamil; Shukur Al-Aeashi

doi:10.24996/ijs.2023.64.10.23

Authors

Enas Mustafa Kamil Department of Mathematics, College of Science for Women, University of Baghdad
Shukur Al-Aeashi Department of Mathematics, College of Education, University of Kufa, Iraq https://orcid.org/0000-0002-9886-3247

DOI:

https://doi.org/10.24996/ijs.2023.64.10.23

Keywords:

ec-closed submodules, generalized extending modules, generalized ECS

Abstract

In this article, we introduce a class of modules that is analogous of generalized extending modules. First we define a module M to be a generalized ECS if and only if for each ec-closed submodule A of M, there exists a direct summand D of M such that is singular, and then we locate generalized ECS between the other extending generalizations. After that we present some of characterizations of generalized ECS condition. Finally, we show that the direct sum of a generalized ECS need not be generalized ECS and deal with decompositions for be generalized ECS concept.