Generalization of Retractable and Coretractable Modules

Nasr Zeyada; O. Al-Mallah; A. Al-Zmammy

doi:10.24297/jam.v8i1.2546

Authors

Nasr Zeyada Cairo University, Faculty of Science, Egypt, King Abdulaziz University, Faculty of Science, Department of Mathematics, Saudi Arabia
O. Al-Mallah King Faisal University, Faculty of Science, Saudi Arabia
A. Al-Zmammy King Faisal University, Faculty of Science, Saudi Arabia

DOI:

https://doi.org/10.24297/jam.v8i1.2546

Keywords:

Retractable Module, s-retractable Module, Coretractable Module, Semi-coretractable Module, Kasch Ring.

Abstract

In this work, we extend the notion of retractability to s- retractability. An R-module is called s-retractable if for all nonzero . Also we extend coretractable modules to semi-coretractable modules. An R-module is called semi-coretractable if for all maximal essential submodule of . We investigate theseclasses of modules and extend some of main theorems on retractable and coretractable modules to s-retractable and semi-coretractable modules, respectively.