⊕-co-coatomically supplemented and co-coatomically semiperfect modules

Abstract

In this paper it is shown that a factor module of an circle plus-co-coatomically supplemented module is not in general circle plus-co-coatomically supplemented. If M is circle plus-co-coatomically supplemented and U is a fully invariant submodule of M then M/U is circle plus-co-coatomically supplemented. A ring R is left perfect if and only if R-(N) is an circle plus-co-coatomically supplemented R-module. A projective module M is co-coatomically semiperfect if and only if M is circle plus-co-coatomically supplemented. A ring is semiperfect if and only if every finitely generated free R-module is co-coatomically semiperfect.