5th China-Japan-Korea International Symposium on Ring Therory 2007, Tokyo, Japan, 10 - 15 September 2007, pp.225-226
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 B(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 is N'- and N ''-Iifting(quasi-discrete).