ON THE RELATIVE (QUASI-)DISCRETENESS OF MODULES

In this paper we investigate the relative (quasi-)discreteness of any module M with respect to any module N. Let 0 → N′ → N → N″ → 0 be an exact sequence and let M be an N-amply supplemented module. Assume that is closed under supplement submodules for every factor module M/T OF M. Then M is N-lifting(quasi-discrete) if and only if M is N′- and N″-lifting(quasi-discrete).