WHEN IS A SIMPLE RING NOETHERIAN

A module M is known to be a CS-module (or an extending module) if ever y complement submodule of M is a direct summand. It is shown that (i) a simple ring R must be right noetherian if every cyclic singular righ t R-module is CS, and (ii) over a simple ring R if every proper cyclic right module is quasi-injective, then R is right hereditary and right noetherian. (C) 1996 Academic Press, Inc.