On Gamma-hyperideals in Gamma-semihypergroup

S. M. AnvariyehS. MirvakiliB. Davvaz



In this paper, the notion of a Γ-hyperideal of a Γ-semihypergroup is introduced. A Γ-hyperideal of a Γ-semihypergroup is a generalization of an ideal of a semigroup, a generalization of a hyperideal of a semihypergroup and a generalization of a Γ−ideal of a Γ-semigroup. Also, we introduce the classes of bi-Γ-hyperideals and quasi Γ-hyperideals of a Γ-semihypergroup and some properties of them are presented. Moreover, quasi simple Γ-hyperideals and minimal Γ-hyperideals in a Γ-semihypergroup are defined, and we investigate the relation between them.

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B. Davvaz, S. M. Anvariyeh, S. Mirvakili