Generalization of Generalized Supplemented Module

In this paper we present the second generalization of generalized supplemented module. This generalization is done through two stages namely, the transition from supplemented into Rad-supplemented followed by transition from Rad-supplemented into weakly Rad-supplemented. If R be a Bass ring and M be a injective module then M is weakly Rad-supplemented module. Also we will generalize the ⊕ -supplemented module into weak⊕ supplemented. We prove that every lifting module is a weak⊕ -supplemented module. These stages depend on the conditions of the modules and rings. Mathematics Subject Classification: 54C05, 54C08, 54C10