On Rad-⊕-Supplemented Modules

Yahya Talebi, Azadeh Mahmoudi

Abstract

Let R be a ring and M a right R-module. M is called Rad-⊕-s-module if every submodule of M has a Rad-supplement that is a direct summand of M, and M is called completely Rad-⊕-s-module if every direct summand of M is Rad-⊕-s-module. In this paper various properties of such modules are developed. It is shown that any finite direct sum of Rad-⊕-s-modules is Rad-⊕-s-module. We also show that if M is Rad-⊕-s-module with (D3), then M is completely Rad-⊕-s-module.