Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X38220120715Applications of epi-retractable modules469477202ENBashishth MuniPandeyaDepartment of Applied Mathematics, Institute of Technology, Banaras Hindu University,
Varanasi-221005, India.Avanish KumarChaturvediDepartment of Mathematics, Jaypee Institute of Information Technology,
(Deemed University) A-10, Sector-62, Noida-201307 (UP), IndiaAshok JiGuptaDepartment of Applied Mathematics, Institute of Technology, Banaras Hindu University,
Varanasi-221005, India.Journal Article20100917An R-module M is called epi-retractable if every submodule of MR is a homomorphic image of M. It is shown that if R is a right perfect ring, then every projective slightly compressible module MR is epi-retractable. If R is a Noetherian ring, then every epi-retractable right R-module has direct sum of uniform submodules. If endomorphism ring of a module MR is von-Neumann regular, 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 if and only if every injective right R-module is semi-simple. A ring R is semi-simple if and only if R is right hereditary and every epiretractable right R-module is projective. Moreover, a ring R is semi-simple if and only if R is a pri and von-Neumann regular.http://bims.iranjournals.ir/article_202_388757ddee7a3a67ab050c9a998e2049.pdf