Kyungpook Mathematical Journal

  • 제62권3호
  • /
  • Pages.407-423
  • /
  • 2022
  • /
  • 1225-6951(pISSN)
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  • 0454-8124(eISSN)
경북대학교 자연과학대학 수학과 (Department of Mathematics, Kyungpook National University)
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On Representable Rings and Modules

  • Mousavi, Seyed Ali (Department of Pure Mathematics, Mahani Mathematical Research Center, Shahid Bahonar University of Kerman) ;
  • Mirzaei, Fatemeh (Department of Pure Mathematics, Mahani Mathematical Research Center, Shahid Bahonar University of Kerman) ;
  • Nekooei, Reza (Department of Pure Mathematics, Mahani Mathematical Research Center, Shahid Bahonar University of Kerman)
  • 투고 : 2020.11.11
  • 심사 : 2021.10.10
  • 발행 : 2022.09.30
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초록

In this paper, we determine the structure of rings that have secondary representation (called representable rings) and give some characterizations of these rings. Also, we characterize Artinian rings in terms of representable rings. Then we introduce completely representable modules, modules every non-zero submodule of which have secondary representation, and give some necessary and sufficient conditions for a module to be completely representable. Finally, we define strongly representable modules and give some conditions under which representable module is strongly representable.

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과제정보

This work was supported by Mahani Mathematical Research Center.

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