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Title: Weakly distributive modules. Applications to supplement submodules
Authors: Büyükaşık, Engin
Demirci, Yılmaz Mehmet
Keywords: Supplement submodule
Distributive module
Commutative ring
Issue Date: Nov-2010
Publisher: Indian Academy of Sciences
Source: Büyükaşık, E., and Demirci, Y. M. (2010). Weakly distributive modules. Applications to supplement submodules. Proceedings of the Indian Academy of Sciences: Mathematical Sciences, 120(5), 525-534. doi:10.1007/s12044-010-0053-9
Abstract: 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.
ISSN: 0253-4142
Appears in Collections:Mathematics / Matematik
Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection

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