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 their injective 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 semilocal rings,
left hereditary rings and left Harada rings.