%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