RAD-circle plus-SUPPLEMENTED MODULES

Abstract

In this paper we provide various properties of Rad-circle plus-supplemented modules. In particular, we prove that a projective module M is Rad-circle plus-supplemented if and only if M is circle plus-supplemented, and then we show that a commutative ring R is an artinian serial ring if and only if every left R-module is Rad-circle plus-supplemented. Moreover, every left R-module has the property (P*) if and only if R is an artinian serial ring and J(2) = 0, where J is the Jacobson radical of R. Finally, we show that every Rad-supplemented module is Rad-circle plus-supplemented over dedekind domains.