Geodesic
The embedding of an ordered semigroup into an le-semigroup
Lobachevskii journal of mathematics, Tome 13 (2003), pp. 45-50

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In this paper we prove the following: If $S$ is an ordered semigroup, then the set $\mathcal P(S)$ of all subsets of $S$ with the multiplication "$\circ$" on $\mathcal P(S)$ defined by "$A\circ B\colon=(AB]$ if $A,B\in\mathcal P(S)$, $A\neq\emptyset$, $B\neq\emptyset$ and $A\circ B\colon=\emptyset$ if $A=\emptyset$ or $B=\emptyset$ is an le-semigroup having a zero element and $S$ is embedded in $\mathcal P(S)$. 
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     author = {N. Kehayopulu and M. Tsingelis},
     title = {The embedding of an ordered semigroup into an le-semigroup},
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N. Kehayopulu; M. Tsingelis. The embedding of an ordered semigroup into an le-semigroup. Lobachevskii journal of mathematics, Tome 13 (2003), pp. 45-50. http://geodesic.mathdoc.fr/item/LJM_2003_13_a4/