APPLICATIONS OF EPI-RETRACTABLE MODULES

An R-module M is called epi-retractable if every sub-module of MR is a homomorphic image of M. It is shown that ifR is a right perfect ring, then every projective slightly compress-ible module MR is epi-retractable. If R is a Noetherian ring, thenevery epi-retractable right R-module has direct sum of uniform sub-modules. If endomorphism ring of a module MR is von-Neumannregular, then M is semi-simple if and only if M is epi-retractable. If R is a quasi Frobenius ring, then R is a right hereditary ring ifand only if every injective right R-module is semi-simple. A ringR is semi-simple if and only if R is right hereditary and every epi-retractable right R-module is projective. Moreover, a ring R issemi-simple if and only if R is pri and von-Neumann regular.