Characterizations of Rad-supplemented modules

Abstract

We prove that a commutative ring R is an artinian principal ideal ring if and only if the ring is semilocal and every Rad-supplemented R-module is a direct sum of w-local R-modules. Moreover, we study of extensions of Rad-supplemented modules over commutative noetherian rings, and we show that if M/N is reduced, M is Rad-supplemented if and only if N and M/N are Rad-supplemented. We also prove that over a dedekind domain an indecomposable, amply Rad-supplemented radical module is hollow radical. © 2012 Miskolc University Press.