On cofinitely ss-supplemented modules

Abstract

In this paper, we introduce the concept of (amply) cofinitely ss-supplemented modules as a proper generalization of (amply) ss-supplemented modules, and we provide various properties of these modules. In particular, we prove that arbitrary sum of cofinitely ss-supplemented modules is cofinitely ss-supplemented. Moreover, we show that a ring \(R\) is semiperfect and \(\operatorname{Rad}(R)\subseteq \operatorname{Soc}(_{R}R)\) if and only if every left \(R\)-module (amply) cofinitely ss-supplemented.