%0 Journal Article %T Applications of epi-retractable modules %J Bulletin of the Iranian Mathematical Society %I Iranian Mathematical Society (IMS) %Z 1017-060X %A Pandeya, Bashishth Muni %A Chaturvedi, Avanish Kumar %A Gupta, Ashok Ji %D 2012 %\ 07/15/2012 %V 38 %N 2 %P 469-477 %! Applications of epi-retractable modules %K Epi-retractable modules %K semi-simple rings %K Perfect rings %K Hereditary rings %K von-Numann regular rings %R %X An 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. %U http://bims.iranjournals.ir/article_202_388757ddee7a3a67ab050c9a998e2049.pdf