A Study on A−I−Γ-Hyperideals and m,n−Γ-Hyperfilters in Ordered Γ-Semihypergroups.

The concept of almost interior Γ -hyperideals (A − I − Γ -hyperideals) in ordered Γ -semihypergroups is a generalization of the concept of interior Γ -hyperideals (I − Γ -hyperideals). In this study, the connections between I − Γ -hyperideals and A − I − Γ -hyperideals in ordered Γ -semihypergroups were presented. Also, we define the notion of m , n - Γ -hyperfilters of ordered Γ -semihypergroups and provide useful results on it. Moreover, we use the weak pseudoorders to construct quotient ordered Γ -semihypergroups by using ordered regular equivalence relations. These concepts lead us to a new research direction in ordered Γ -semihypergroups. [ABSTRACT FROM AUTHOR]