Two Generalizations of Lifting Modules

In this paper we introduce the notions of G1L-modules and G2Lmodules which are two proper generalizations of lifting modules. Then we give some characterizations and properties of these modules. We also show that these two classes of modules are not closed under direct sums. Some special cases of direct sums of these modules are studied. Moreover, Harada rings are characterized by using G1L-modules.