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 circle plus-cofinitely supplemented modules. In particular, we prove that a pi-projective module M is a cms-module if and only if M is circle divide-cofinitely supplemented. Finally, we show that every free R-module is a cms-module if and only if R is semiperfect.