A generalization of ?-cofinitely supplemented modules

Abstract

We say that a module M is a cms-module if, for every cofinite submodule N of M, there exist submodules K and K? of M such that K is a supplement of N, and K, K? are mutual supplements in M. In this article, the various properties of cms-modules are given as a generalization of ?-cofinitely supplemented modules. In particular, we prove that a ?-projective module M is a cms-module if and only if M is ?-cofinitely supplemented. Finally, we show that every free R-module is a cms-module if and only if R is semiperfect. © 2016 Iranian Mathematical Society.