# The embedding of an ordered semigroup into an le-semigroup

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

In this paper we prove the following: If *S* is an ordered semigroup, then the set * P (S)* of all subsets of *S* with the multiplication *"º"* on * P(S)* defined by *"Aº B: = (AB]* if *A, B∈ P(S)*, *A≠ ∅*, *B≠ ∅* and *Aº B: =∅* if *A = ∅* or *B=∅* is an le-semigroup having a zero element and *S* is embedded in * P(S)*.