# A note on minimal and maximal ideals of ordered semigroups

## (*Lobachevskii Journal of Mathematics, Volume XI*)

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 ∈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*.