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H-supplemented modules with respect to images of fully invariant submodules

  • Moniri Hamzekolaee, A. R. [1] ; Amouzegar, Tayyebeh [2]
    1. [1] University of Mazandaran

      University of Mazandaran

      Irán

    2. [2] University of Technology

      University of Technology

      Rusia

  • Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 40, Nº. 1, 2021, págs. 35-48
  • Idioma: inglés
  • DOI: 10.22199/issn.0717-6279-2021-01-0003
  • Enlaces
  • Resumen
    • Lifting modules plays important roles in module theory. H-supplemented modules are a nice generalization of lifting modules which have been studied extensively recently. In this article, we introduce a proper generalization of H-supplemented modules via images of fully invariant submodules. Let F be a fully invariant submodule of a right Rmodule M. We say that M is IF -H-supplemented in case for every endomorphism φ of M, there is a direct summand D of M such that φ(F) + X = M if and only if D + X = M, for every submodule X of M. It is proved that M is IF -H-supplemented if and only if F is a dual Rickart direct summand of M for a fully invariant noncosingular submodule F of M. It is shown that the direct sum of IF –H supplemented modules is not in general IF -H-supplemented. Some sufficient conditions such that the direct sum of IF -H-supplemented modules is IF -H-supplemented are given

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