A generalization of ⊕-cofinitely supplemented modules
Bulletin of the Iranian Mathematical Society, cilt.42, sa.1, ss.91-99, 2016 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 42 Sayı: 1
- Basım Tarihi: 2016
- Dergi Adı: Bulletin of the Iranian Mathematical Society
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Sayfa Sayıları: ss.91-99
- Anahtar Kelimeler: (⊕-)cofinitely supplemented module, Cofinite submodule, Supplements
- Ondokuz Mayıs Üniversitesi Adresli: Evet
Özet
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.