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Citation - WoS: 5
Citation - Scopus: 8
Weakly Distributive Modules. Applications To Supplement Submodules
(Indian Academy of Sciences, 2010) Büyükaşık, Engin; Demirci, Yılmaz Mehmet
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 π-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 ⊕-supplemented module is quasi-discrete. © Indian Academy of Sciences.
Citation - WoS: 8
Citation - Scopus: 8
Modules Whose Maximal Submodules Are Supplements
(Hacettepe Üniversitesi, 2010) Büyükaşık, Engin; Pusat, Dilek
We study modules whose maximal submodules are supplements (direct summands). For a locally projective module, we prove that every maximal submodule is a direct summand if and only if it is semisimple and projective. We give a complete characterization of the modules whose maximal submodules are supplements over Dedekind domains.

Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection