Weakly distributive modules. Applications to supplement submodules

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Buyukasik E., DEMİRCİ Y. M.

PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES, vol.120, no.5, pp.525-534, 2010 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 120 Issue: 5
  • Publication Date: 2010
  • Doi Number: 10.1007/s12044-010-0053-9
  • Journal Name: PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.525-534
  • Keywords: Distributive module, supplement submodule
  • Abdullah Gül University Affiliated: No

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 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.