On completely regular 2-duo ordered semihypergroups

Abstract

The concept of duo ordered semihypergroups was introduced by Ardekani and Davvaz in 2018. In this paper, we introduce the concept of n-duo ordered semihypergroups. We show that every duo ordered semihypergroup is an n-duo ordered semihypergroup (n ≥ 2),  but the converse is not generally true. We investigate the concept of completely regular 2-duo ordered semihypergroups and give their characterizations in terms of (2, 0) -hyperideals, (0, 2) -hyperideals, (2, 2) -hyperideals and (2, 2) -quasi-hyperideals. Finally, we show that in 2-duo ordered semihypergroups, every (2, 2) -hyperideal is quasi-prime.