On generalization of Rad-$D_{11}$-module

Abstract

This paper gives generalization of a notion of supplemented module. Here, we utilize some algebraic properties like supplemented, amply supplemented and local modules in order to obtain the generalization. Other properties that are instrumental in this generalization are $D_{i}$, $SSP$ and $SIP$. If a module $M$ is $Rad$-$D_{11}$-module and has $D_{3}$ property, then $M$ is said to be completely-$Rad$-$D_{11}$-module ($C$-$Rad$-$D_{11}$-module). Similarly it is for $M$ with $SSP$ property. We provide some conditions for a supplemented module to be $C$-$Rad$-$D_{11}$-module.