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BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY, vol.42, no.1, pp.91-99, 2016 (SCI-Expanded)
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.