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

Abstract

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