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Ukrainian Mathematical Journal

, Volume 63, Issue 5, pp 768–775 | Cite as

On strongly ⊕-supplemented modules

  • C. Nebiyev
  • A. Pancar
Article
  • 45 Downloads

Strongly ⊕-supplemented and strongly cofinitely ⊕-supplemented modules are defined and some properties of strongly ⊕-supplemented and strongly cofinitely ⊕-supplemented modules are investigated. Let R be a ring. Then every R-module is strongly ⊕-supplemented if and only if R is perfect. The finite direct sum of ⊕-supplemented modules is ⊕-supplemented. However, this is not true for strongly ⊕-supplemented modules. Any direct sum of cofinitely ⊕-supplemented modules is cofinitely ⊕-supplemented but this is not true for strongly cofinitely ⊕-supplemented modules. We also prove that a supplemented module is strongly ⊕-supplemented if and only if every supplement submodule lies above a direct summand.

Keywords

Direct Summand Left Ideal Projective Module Projective Cover Discrete Valuation Ring 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media, Inc. 2011

Authors and Affiliations

  • C. Nebiyev
    • 1
  • A. Pancar
    • 1
  1. 1.SamsunTurkey

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