On C. lifting and Semi*perfect Modules

In this paper, we introduce c. lifting module as a generalization of lifting module, we prove some results on c. lifting module, also we introduce semi*perfect module as a generalization of a semiperfect module and direct summand generalized* co-finitely weakly supplemented module as a generalization of a direct summand co-finitely weakly supplemented module and we prove under certain conditions c. lifting, semi*perfect and direct summand generalized* co- finitely weakly supplemented modules are equivalent. Keywords:lifting modules,co-finitely semiperfect modules, direct summand supplemented modules, generalization of lifting modules and generalization of a generalized weakly supplemented modules