Amply weak semisimple-supplemented modules

Abstract

Let R be a ring and M be a right R-module. In this paper we will study various properties of amply weak semisimple-supplemented module. It is shown that: (1) every projective weakly semisimple-supplemented module is amply weak semisimple-supplemented; (2) if M is an amply weak semisimplesupplemented module and satisfies DCC on weak semisimple-supplement submodules and on small submodules, then M is Artinian; (3) an amply weak semisimple-supplemented module behaves well with respect to supplements and to homomorphic images