## M. Arslanov, N. Kehayopulu

## A note on minimal and maximal ideals of ordered
semigroups

## (Lobachevskii Journal of Mathematics, Vol.11, pp.3-6)

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 $S$.

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