On a class of perfect rings

A module $M$ is called ss-semilocal if every submodule $U$ of $M$ has a weak supplement $V$ in $M$ such that $U \cap V$ is semisimple. In this paper, we provide the basic properties of ss-semilocal modules. In particular, it is proved that, for a ring $R$, $_{R}R$ is $ss$-semilocal if and only if every left $R$-module is $ss$-semilocal if and only if $R$ is semilocal and $Rad(R)\subseteq Soc(_{R}R)$. We define projective $ss$-covers and prove the rings with the property that every (simple) module has a projective $ss$-cover are $ss$-semilocal. KCI Citation Count: 0