Strongly ⊕−g−radical supplemented modules

Abstract

. In this work, strongly ⊕ − g − radical supplemented modules are defined 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 ⊕− g − radical supplemented module is strongly ⊕− g − radical supplemented. Let f : M −→ N be an R − module epimorphism and Ker ( f ) be a direct summand of M . If M is strongly ⊕− g − radical supplemented, then N is also strongly ⊕− g − radical supplemented. Let M be a strongly ⊕− g − radical supplemented R − module 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 ⊕− g − radical supplemented.