On certain Γ-hyperideals in Γ-semihypergroups

Document Type : Research Paper

Authors

1 Department of Mathematics, S.N.J.B.’s K.K.H.A. Arts, S.M.G.L. Commerce & S.P.H.J. Science College, Chandwad, District Nashik, 423 101, M.S., India

2 Department of Mathematics, School of Mathematical Sciences, Kavayitri Bahinabai Chaudhari North Maharashtra University, Jalgaon, 425 001 M.S., India

Abstract

In this paper pseudo symmetric Γ-hyperideal in Γsemihypergroups is introduced and characterized. It is proved that
the class of pseudo symmetric Γ-semihypergroups contains left (right) duo Γ-semihypergroups, quasi commutative Γ-semihypergroups with unity, left (right) pseudo commutative Γ-semihypergroups and idempotent Γ-semihypergroups. The notions of completely prime Γhyperideal, semiprime Γ-hyperideal, partially semiprime Γ- hyperideal are also defined and completely prime Γ-hyperideal of a Γsemihypergroup has been characterized in terms of prime Γ- hyperideal and pseudo symmetric Γ-hyperideal. The characterization of completely semiprime Γ-hyperideals of Γ-semihypergroups
is presented. In Γ-semihypergroup n-semiprime Γ-hyperideal and npartially semiprime Γ-hyperideal are introduced as a generalization of semiprime Γ-hyperideal and partially semiprime Γ-hyperideal of Γ-semihypergroup respectively. The notion of semi-extension of Γhyperideal in Γ-semihypergroup has also been defined. Some related results are proved along with establishing the relationship between n-semiprime Γ-hyperideals and semi-extension of Γ-hyperideal in commutative Γ-semihypergroups.

Keywords

References

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Journal of Hyperstructures
Volume 9, Issue 2
December 2020
Pages 34-51

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