Abstract

In this work, strongly gradical supplemented modules are de…ned and some properties of these modules are investigated. Every ring has unity and every module is unital left module in this work. It is proved that every direct summand of a strongly gradical supplemented module is strongly gradical supplemented. Let f : M ! N be an Rmodule epimorphism and Ker (f) be a direct summand of M. If M is strongly gradical supplemented, then N is also strongly gradical supplemented. Let M be a strongly gradical supplemented Rmodule and K M. If V is a g-radical supplement submodule in M for every g-radical supplement submodule V =K in M=K, then M=K is strongly gradical supplemented.