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

  • Abbasi, M.Y. (Department of Mathematics, Jamia Millia Islamia) ;
  • Basar, A. (Department of Mathematics, Jamia Millia Islamia) ;
  • Talee, A.F. (Department of Mathematics, Jamia Millia Islamia) ;
  • Khan, S.A. (Department of Mathematics, Jamia Millia Islamia, Mohammad Ali Jauhar)
  • Received : 2017.10.24
  • Accepted : 2017.12.08
  • Published : 2018.03.25

Abstract

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.

Keywords

${\Gamma}$-semihypergroups;soft intersection ${\Gamma}$-hyperideals;regular and simple ${\Gamma}$-semihypergroups

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