Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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On Regular Γ-semihyperrings and Idempotent 𝚪-semihyperrings

  • Pawar, Kishor Fakira (Department of Mathematics, School of Mathematical Sciences, Kavayitri Bahinabai Chaudhari North Maharashtra University) ;
  • Patil, Jitendra Jaysing (Department of Mathematics, Indraraj Arts, Commerce & Science College) ;
  • Davvaz, Bijan (Department of Mathematics, Yazd University)
  • Received : 2017.04.06
  • Accepted : 2019.01.21
  • Published : 2019.03.23
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Abstract

The ${\Gamma}$-semihyperring is a generalization of the concepts of a semiring, a semihyperring and a ${\Gamma}$-semiring. Here, the notions of (strongly) regular ${\Gamma}$-semihyperring, idempotent ${\Gamma}$-semihyperring; invertible set, invertible element in a ${\Gamma}$-semihyperring are introduced, and several examples given. It is proved that if all subsets of ${\Gamma}$-semihyperring are strongly regular then for every ${\Delta}{\subseteq}{\Gamma}$, there is a ${\Delta}$-idempotent subset of R. Regularity conditions of ${\Gamma}$-semihyperrings in terms of ideals of ${\Gamma}$-semihyperrings are also characterized.

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References

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