Generalizations of ss-supplemented modules

Abstract

We introduce the concept of (strongly) ss-radical supplemented modules. We prove that if a submodule N of M is strongly ss-radical supplemented and Rad(M/ N) = M/ N, then M is strongly ss-radical supplemented. For a left good ring R, we show that Rad(R) C Soc(RR) if and only if every left R-module is ss-radical supplemented. We characterize the rings over which all modules are strongly ss-radical supplemented. We also prove that over a left WV-ring every supplemented module is ss-supplemented.