## 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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