CO-EPI-FINITE-RETRACTABLE RING AND MODULE

Recall that an R-module M is said to be co-epi-finite-retractable (simply CEFR) whenever for every finitely generated submodule N of M, the factor module M/N can be embedded in M. We find conditions under which free modules are CEFR. We show that, if RM is both a CEFR and endoregular module, then it is a regular module. We also examine rings in which every R_x0002_module is CEFR, referred to as CEFR rings. We investigate, every R-module is CEFR if and only if every CFR module is a CEFR module.