Kyungpook Mathematical Journal

  • 제51권4호
  • /
  • Pages.375-384
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  • 2011
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  • 1225-6951(pISSN)
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  • 0454-8124(eISSN)
경북대학교 자연과학대학 수학과 (Department of Mathematics, Kyungpook National University)
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Baer and Quasi-Baer Modules over Some Classes of Rings

  • Haily, Abdelfattah (Departement de Mathematiques et Informatique, Faculte des Sciences) ;
  • Rahnaou, Hamid (Departement de Mathematiques et Informatique, Faculte des Sciences)
  • 투고 : 2011.01.27
  • 심사 : 2011.08.21
  • 발행 : 2011.11.23
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초록

We study Baer and quasi-Baer modules over some classes of rings. We also introduce a new class of modules called AI-modules, in which the kernel of every nonzero endomorphism is contained in a proper direct summand. The main results obtained here are: (1) A module is Baer iff it is an AI-module and has SSIP. (2) For a perfect ring R, the direct sum of Baer modules is Baer iff R is primary decomposable. (3) Every injective R-module is quasi-Baer iff R is a QI-ring.

키워드

참고문헌

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피인용 문헌

  1. On weak Rickart modules vol.16, pp.09, 2017, https://doi.org/10.1142/S0219498817501651
  2. Direct sums of quasi-Baer modules vol.456, 2016, https://doi.org/10.1016/j.jalgebra.2016.01.039
  3. Weak Rickart and dual weak Rickart objects in abelian categories vol.46, pp.7, 2018, https://doi.org/10.1080/00927872.2017.1404079