SS-radical supplemented modules and strongly SS-radical supplemented modules

In this study, are introduced ss-radical supplemented modules and 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 prove that for inclusion of rad (R) in the socle of the R left R-module if and only if every left R-module is ss-radical supplemented. If R is a left WV-ring, then every left R-module is ss-radical supplemented. We have characterized the rings over which all modules are strongly ss-radical supplemented. Moreover, we determine the structure of (strongly) ss-radical supplemented modules over a local Dedekind domain.