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.