Weakly distributive modules. Applications to supplement submodules
PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES, cilt.120, sa.5, ss.525-534, 2010 (SCI-Expanded)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 120 Sayı: 5
- Basım Tarihi: 2010
- Doi Numarası: 10.1007/s12044-010-0053-9
- Dergi Adı: PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Sayfa Sayıları: ss.525-534
- Anahtar Kelimeler: Distributive module, supplement submodule
- Abdullah Gül Üniversitesi Adresli: Hayır
Özet
In this paper, we define and study weakly distributive modules as a proper generalization of distributive modules. We prove that, weakly distributive supplemented modules are amply supplemented. In a weakly distributive supplemented module every submodule has a unique coclosure. This generalizes a result of Ganesan and Vanaja. We prove that pi-projective duo modules, in particular commutative rings, are weakly distributive. Using this result we obtain that in a commutative ring supplements are unique. This generalizes a result of Camillo and Lima. We also prove that any weakly distributive circle plus-supplemented module is quasi-discrete.