Rad-supplements in injective modules

Abstract

We introduce and study the notion of Rad-s-injective modules (i.e. modules which are Rad-supplements in the irinjective hulls). We compare this notion with another generalization of injective modules. We show that the class of Rad-s-injective modules is closed under finite direct sums. We characterize Rad-s-injective modules over several type of rings, including semilocalrings, left hereditary rings and left Harada rings.