In this paper , we introduce * relation on the Lattic of submodules of a module M. We say that submodule X ,Y of M are * equivalent , X * Y, if + + and + + ,for some H≪TM .We show that * relation is an equivalence relation and has good behavior with respect to addition of submodules and homomorphisms. This relation is used to define and study the class of Goldie*-T-lifting modules.
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