A study on \(A-I-\Gamma\)-hyperideals and \((m, n)-\Gamma\)-hyperfilters in ordered \(\Gamma\)-semihypergroups
Summary: The concept of almost interior \(\Gamma\)-hyperideals \((A-\mathbf{I}-\Gamma\)-hyperideals) in ordered \(\Gamma\)-semihypergroups is a generalization of the concept of interior \(\Gamma\)-hyperideals \((\mathbf{I}-\Gamma\)-hyperideals). In this study, the connections between \(\mathbf{I}-\Gamma\)-hyperideals and \(A-\mathbf{I}-\Gamma\)-hyperideals in ordered \(\Gamma\)-semihypergroups were presented. Also, we define the notion of \((m, n)\)-\(\Gamma\)-hyperfilters of ordered \(\Gamma\)-semihypergroups and provide useful results on it. Moreover, we use the weak pseudoorders to construct quotient ordered \(\Gamma\)-semihypergroups by using ordered regular equivalence relations. These concepts lead us to a new research direction in ordered \(\Gamma\)-semihypergroups.
scientific article; zbMATH DE number 7367244
scientific article