Green's relations on ordered n-ary semihypergroups

Abstract

In this paper, we introduce the concept of weak $i$-hyperfilters of ordered $n$-arysemihypergroups, where a positive integer 1 ≤ i ≤ n and n ≥ 2, 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