Semisimple Modules Relative to A Semiradical Property

Entisar Ahmed Mohammad Al - Dhaheri; Bahar Hamad Al - Bahrani

doi:10.24996/ijs.2022.63.11.26

Authors

Entisar Ahmed Mohammad Al - Dhaheri Department of Mathematics, College of Science, University of Baghdad, Baghdad, Iraq https://orcid.org/0000-0002-4428-5082
Bahar Hamad Al - Bahrani Department of Mathematics, College of Science, University of Baghdad, Baghdad, Iraq

DOI:

https://doi.org/10.24996/ijs.2022.63.11.26

Keywords:

Semiradical (radical) property, Semisimple modules, t- semisimple modules

Abstract

In this paper, we introduce the concept of s.p-semisimple module. Let S be a semiradical property, we say that a module M is s.p - semisimple if for every submodule N of M, there exists a direct summand K of M such that K ≤ N and N / K has S. we prove that a module M is s.p - semisimple module if and only if for every submodule A of M, there exists a direct summand B of M such that A = B + C and C has S. Also, we prove that for a module M is s.p - semisimple if and only if for every submodule A of M, there exists an idempotent e ∊ End(M) such that e(M) ≤ A and (1- e)(A) has S.