%0 Journal Article
%T Applications of Epi-Retractable and Co-Epi-Retractable Modules
%J Bulletin of the Iranian Mathematical Society
%I Iranian Mathematical Society (IMS)
%Z 1017-060X
%A Mostafanasab, H.
%D 2013
%\ 10/15/2013
%V 39
%N 5
%P 903-917
%! Applications of Epi-Retractable and Co-Epi-Retractable Modules
%K MSC(2010): Primary: 16D10, 16S50
%K Secondary: 16D40, 16E60
%R
%X A module M is called epi-retractable if every submodule of M is a homomorphic image of M. Dually, a module M is called co-epi-retractable if it contains a copy of each of its factor modules. In special case, a ring R is called co-pli (resp. co-pri) if RR (resp. RR) is co-epi-retractable. It is proved that if R is a left principal right duo ring, then every left ideal of R is an epi-retractable R-module. A co-pli strongly prime ring R is a simple ring. A left self-injective co-pli ring R is left Noetherian if and only if R is a left perfect ring. It is shown that a cogenerator ring R is a pli ring if and only if it is a co-pri ring. Moreover, if R is a left perfect ring such that every projective R-module is co-epi-retractable, then R is a quasi-Frobenius ring.
%U http://bims.iranjournals.ir/article_451_a85b04c9d7350c032000bab9ef5951af.pdf