Green's relations on ordered n-ary semihypergroups

In this paper, we introduce the concept of weak i-hyperfilters of ordered n-arysemihypergroups, where a positive integer ۱ ≤ i ≤ n and n ≥ ۲, and then discuss theirrelated properties. We define the Green’s relations M_i, J , H and K on ordered n-arysemihypergroups and investigate the relationships between the Green’s relations and theequivalence relation W_i, which is generated by the weak i-hyperfilters. Also, we givethe characterizations of intra-regular ordered n-ary semihypergroups via the propertiesof weak i-hyperfilters. Finally, we introduce the concepts of (i-, Λ-)duo ordered n-arysemihypergroups and establish some interesting properties.

Keywords:

ordered n-ary semihypergroup , hyperfilter , Green’s relations , intra-regular element