The ordered semilattice equivalence relations on ordered semihypergroups

Abstract

The semilattice equivalence relations play an important role in investigating the structural properties of ordered semihypergroups. Such relations can be expressed in terms of hyperfilters. There are two concepts of (ordered) hyperfilters of (ordered) semihypergroups which were introduced by Tang et al. [16] and Kehayopulu[9]. In this paper, we prove that those two concepts coincide and characterize the least semilattice equivalence relations on ordered semi-hypergroups. Furthermore, we investigate the relationship between the semilattice equivalence relations and the strongly ordered regular equivalence relations on ordered semihypergroups. Finally, we introduce the concept of ρ-classes-chain on ordered semihypergroups and give the characterization of the strongly ordered regular equivalence relations via such concept.