s-WH Modules

Osama Basim  Mohammed; Thaar Younis  Ghawi

doi:10.24996/ijs.2024.65.10.29

Authors

Osama Basim Mohammed Department of Mathematics, College of Education, AL-Qadisiyah University, AL-Qadisiyah, Iraq https://orcid.org/0000-0003-4325-5305
Thaar Younis Ghawi Department of Mathematics, College of Education, AL-Qadisiyah University, AL-Qadisiyah, Iraq https://orcid.org/0000-0002-0637-1908

DOI:

https://doi.org/10.24996/ijs.2024.65.10.29

Keywords:

s-WH modules, Hopfian modules, weakly Hopfian modules, e-small submodules

Abstract

This article introduces the concept of strongly-WH module which is a proper generalized of Hopfian modules. A module is called strongly-WH, briefly -WH if, any -small surjective -endomorphism of is an automorphism. We specify and provide some properties of this concept. Furthermore, we have established connections between strongly-WH modules and various other concepts. We demonstrate that every strongly-WH module is -weakly Hopfian. As well as, we provide cases in which the concepts of WH, -weakly Hopfian, and strongly-WH modules are equivalent.