• 제목/요약/키워드: regular and simple ${\Gamma}$-semihypergroups

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GENERALIZED((ξ, ζ)-) SOFT INTERIOR Γ-HYPERIDEALS OF Γ-SEMIHYPERGROUPS

  • Abbasi, M.Y.;Basar, A.;Talee, A.F.;Khan, S.A.
    • 호남수학학술지
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    • 제40권1호
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    • pp.93-108
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    • 2018
  • In this paper, we introduce the notion of ($\xi$, ${\zeta}$)-soft ${\Gamma}$-hyperideals and ($\xi$, ${\zeta}$)-soft interior ${\Gamma}$-hyperideals of ${\Gamma}$-semihypergroups by a new approach called soft intersection (briefly, S. I.). It is proved that in regular ${\Gamma}$-semihypergroups the ($\xi$, ${\zeta}$)-soft ${\Gamma}$-hyperideals and the ($\xi$, ${\zeta}$)-soft interior ${\Gamma}$-hyperideals coincide. Further, we introduce the concept of ($\xi$, ${\zeta}$)-soft simple ${\Gamma}$-semihypergroup and characterize the simple ${\Gamma}$-semihypergroups in terms of ($\xi$, ${\zeta}$)-soft ${\Gamma}$-hyperideals and ($\xi$, ${\zeta}$)-soft interior ${\Gamma}$-hyperideals.