Abstract :
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 (respectively,
co-pri) if $_{R}R$ (respectively, $R_{R}$) 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.
