Some properties of weakly r-supplemented modules
Logic Journal of the IGPL, cilt.34, sa.3, 2026 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 34 Sayı: 3
- Basım Tarihi: 2026
- Doi Numarası: 10.1093/jigpal/jzag017
- Dergi Adı: Logic Journal of the IGPL
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Applied Science & Technology Source, Compendex, INSPEC, MathSciNet, zbMATH, Business Source Ultimate (EBSCO)
- Anahtar Kelimeler: r-small submodules, r-supplemented modules, radical, small submodules
- Ondokuz Mayıs Üniversitesi Adresli: Evet
Özet
In this study, we introduce and examine the concept of weakly r-supplemented modules and establish several fundamental properties concerning them. It is shown that if the radical of a weakly supplemented module (Formula presented) serves as a supplement submodule in (Formula presented), then (Formula presented) is necessarily weakly r-supplemented. We also demonstrate that every factor module, every homomorphic image, and every r-small cover of a weakly r-supplemented module inherit the weakly r-supplemented property. Moreover, if a module (Formula presented) can be written as the sum (Formula presented) where each (Formula presented) ((Formula presented) ) is weakly r-supplemented, then (Formula presented) itself enjoys the same property. Finally, it is established that whenever (Formula presented) is weakly r-supplemented, any finitely (Formula presented) -generated (Formula presented) -module is also weakly r-supplemented.