Indexed on: 01 Mar '05Published on: 01 Mar '05Published in: Siberian Mathematical Journal
It is well known that a projective module M is ⊕-supplemented if and only if M is semiperfect. We show that a projective module M is ⊕-cofinitely supplemented if and only if M is cofinitely semiperfect or briefly cof-semiperfect (i.e., each finitely generated factor module of M has a projective cover). In this paper we give various properties of the cof-semiperfect modules. If a projective module M is semiperfect then every M-generated module is cof-semiperfect. A ring R is semiperfect if and only if every free R-module is cof-semiperfect.