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Weakly distributive modules. Applications to supplement submodules

  • Engin Büyükaşık
  • Yılmaz M. Demirci
Article

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.

Keywords

Distributive module supplement submodule 

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Copyright information

© Indian Academy of Sciences 2010

Authors and Affiliations

  1. 1.Department of MathematicsIzmir Institute of TechnologyUrla, IzmirTurkey

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