A note on minimal and maximal ideals of ordered semigroups

Ideals of ordered groupoids were defined by second author in [2]. Considering the question under what conditions an ordered semigroup (or semigroup) contains at most one maximal ideal we prove that in an ordered groupoid $S$ without zero there is at most one minimal ideal which is the intersection of all ideals of $S$. In an ordered semigroup, for which there exists an element a $\in S$ such that the ideal of $S$ generated by $a$ is $S$, there is at most one maximal ideal which is the union of all proper ideals of $S$. In ordered semigroups containing unit, there is at most one maximal ideal which is the union of all proper ideals of $S$.