Niovi Kehayopulu and Michael Tsingelis

The embedding of an ordered semigroup into an le-semigroup

(Lobachevskii Journal of Mathematics, Vol.13, pp.45-50)

In this paper we prove the following: If $S$ is an ordered semigroup, then the set ${\cal P} (S)$ of all subsets of $S$ with the multiplication $"\circ"$ on ${\cal P}(S)$ defined by $"A\circ B: = (AB]$ if $A, B\in {\cal P}(S)$, $A\neq \emptyset$, $B\neq \emptyset$ and $A\circ B: =\emptyset$ if $A = \emptyset$ or $B=\emptyset$ is an le-semigroup having a zero element and $S$ is embedded in ${\cal P}(S)$.



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