Rings whose modules are weakly supplemented are perfect. Applications to certain ring extensions - Büyükasik, Engin; Lomp, Christian (MATHEMATICA SCANDINAVICA, 2009)
In this note we show that a ring $R$ is left perfect if and only if every left $R$-module is weakly supplemented if and only if $R$ is semilocal and the radical of the countably infinite free left $R$-module has a weak supplement.