ON THE RELATIVE (QUASI-)DISCRETENESS OFMODULES

摘要

In this paper we investigate the relative (quasi-)discreteness of any module Mwith respect to any module N. Let 0 N N" 0 be anexact sequence and let M be an N-amply supplemented module. Assume that13(M/T, N) 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 isandN"-lifting(quasi-discrete).