A generalization of ⊕-cofinitely supplemented modules
Bulletin of the Iranian Mathematical Society, vol.42, no.1, pp.91-99, 2016 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 42 Issue: 1
- Publication Date: 2016
- Journal Name: Bulletin of the Iranian Mathematical Society
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Page Numbers: pp.91-99
- Keywords: (⊕-)cofinitely supplemented module, Cofinite submodule, Supplements
- Ondokuz Mayıs University Affiliated: Yes
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 π-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.