A variation of -lifting and -supplemented modules with respect to an equivalence relation

n this paper we introduce Goldie--supplemented modules as follows. A module is called Goldie--supplemented (briefly, G -supplemented) if there exists a -supplement of for every submodule of such that . We say that a module is called Goldie--lifting (briefly, G -lifting) if there exists a direct summand of for every submodule of such that . Note that the last concept given in [4] as a --supplemented module. We present fundamental properties of these modules. We indicate that these modules lie between -lifting and -supplemented modules. Also we prove that our modules coincide with some variations of -supplemented modules for -semiperfect modules.