Characterization of Ordered Semihypergroups by Covered Hyperideals

Md Firoj Ali, Noor Mohammad Khan

After introducing the notions of the Green's relation $\mathcal{J}$, hyper $\mathcal{J}$-class and covered hyperideal in an ordered semihypergroup, some important properties of the hyper $\mathcal{J}$-class and covered hyperideals are studied. Then maximal and minimal hyperideals of an ordered semihypergroup are defined and some vital results have been proved. We also define a hyperbase of an ordered semihypergroup and prove the existence of a hyperbase under certain conditions in an ordered semihypergroup. In an ordered semihypergroup, after defining the greatest covered hyperideal and the greatest hyperideal, some results about these hyperideals are proved. Finally, in a regular ordered semihypergroup, we show that, under some conditions, each hyperideal is also a covered hyperideal.