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

TL;DR

This paper extends the concept of Rad-$D_{11}$-modules by incorporating properties like supplemented, amply supplemented, and local modules, providing new conditions for modules to be classified as completely Rad-$D_{11}$-modules.

Contribution

It introduces a generalization of Rad-$D_{11}$-modules using algebraic properties such as $D_{i}$, $SSP$, and $SIP$, and establishes conditions for modules to be classified as completely Rad-$D_{11}$-modules.

Findings

Defined the notion of completely Rad-$D_{11}$-modules.

Provided conditions for supplemented modules to be completely Rad-$D_{11}$-modules.

Connected properties like $D_{3}$, $SSP$, and $SIP$ to the generalization.

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.