Semi-Essentially Compressible Modules and Semi-Essentially Retractable Modules

Mohammed Baqer Hashim Al Hakeem; Nuhad Salim Al-Mothafar

doi:10.24996/ijs.2023.64.4.26

Authors

Mohammed Baqer Hashim Al Hakeem Department of Mathematics, college of Science, Baghdad University, Baghdad, Iraq
Nuhad Salim Al-Mothafar Department of Mathematics, college of Science, Baghdad University, Baghdad, Iraq

DOI:

https://doi.org/10.24996/ijs.2023.64.4.26

Keywords:

Compressible module, Retractable module, Essential compressible module, Essential retractable module, Semi- essential compressible, Semi- essential retractable

Abstract

Let be a commutative ring with 1 and be a left unitary . In this paper, the generalizations for the notions of compressible module and retractable module are given.

An is termed to be semi-essentially compressible if can be embedded in every of a non-zero semi-essential submodules. An is termed a semi-essentially retractable module, if for every non-zero semi-essentially submodule of an . Some of their advantages characterizations and examples are given. We also study the relation between these classes and some other classes of modules.