Abstract

Let R be a ring and M a right R-module. In this note, we show that a quotient of an -cofinitely supplemented module is not in general -cofinitely supplemented and prove that if a module M is an -cofinitely supplemented multiplication module with Rad(M)M, then M can be written as an irredundant sum of local direct summand of M. An extension of the result of Calisici and Pancar [1], here it is shown that an arbitrary module is cofinitely semiperfect if and only if it is an (amply) cofinitely supplemented by supplements which have projective covers.