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

Abstract

The concept of almost interior $\mathrm{\Gamma }$ -hyperideals ( $A-\mathbf{I}-\mathrm{\Gamma }$ -hyperideals) in ordered $\mathrm{\Gamma }$ -semihypergroups is a generalization of the concept of interior $\mathrm{\Gamma }$ -hyperideals ( $\mathbf{I}-\mathrm{\Gamma }$ -hyperideals). In this study, the connections between $\mathbf{I}-\mathrm{\Gamma }$ -hyperideals and $A-\mathbf{I}-\mathrm{\Gamma }$ -hyperideals in ordered $\mathrm{\Gamma }$ -semihypergroups were presented. Also, we define the notion of $\left(m,n\right)$ - $\mathrm{\Gamma }$ -hyperfilters of ordered $\mathrm{\Gamma }$ -semihypergroups and provide useful results on it. Moreover, we use the weak pseudoorders to construct quotient ordered $\mathrm{\Gamma }$ -semihypergroups by using ordered regular equivalence relations. These concepts lead us to a new research direction in ordered $\mathrm{\Gamma }$ -semihypergroups.