Ordered semigroups which are both right commutative and right cancellative

In this paper we prove that each right commutative, right cancellative ordered semigroup (S,.,??) can be embedded into a right cancellative ordered semigroup (T,??,?) such that (T,??) is left simple and right commutative. As a consequence, an ordered semigroup S which is both right commutative and right cancellative is embedded into an ordered semigroup T which is union of pairwise disjoint abelian groups, indexed by a left zero subsemigroup of?T.