International Journal of Mathematics and Mathematical Sciences
Volume 2007 (2007), Article ID 10836, 5 pages
doi:10.1155/2007/10836

A Note on ⊕-Cofinitely Supplemented Modules

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.