Green s relations on ordered n-ary semihypergroups

In this paper, we introduce the concept of weak i-hyperfilters of ordered n-ary semihypergroups, where a positive integer 1 ≤ i ≤ n and n ≥ 2, and discuss their related properties. We define Green’s relations Mi, J , H and K on ordered n-ary semihypergroups and investigate the relationships between Green’s relations and the equivalence relation Wi, which is generated by the weak i-hyperfilters. Also, we give the characterizations of intra-regular ordered n-ary semihypergroups via the properties of weak ihyperfilters. Finally, we introduce the concepts of (i-, Λ-)duo ordered n-ary semihypergroups and establish some interesting properties.