The embedding of some ordered semigroups into ordered groups (Q1976425)

Let \(S\) be an ordered semigroup. \(S\) is called cancellative if \(ca\leq cb\) implies \(a\leq b\) and \(ac\leq bc\) implies \(a\leq b.\) \(S\) is called right reversible if \(Sa\cap Sb\not=\emptyset.\) The authors prove that any right reversible, callellative ordered semigroup can be embedded in an ordered group. As a consequence, a commutative ordered semigroup is embedded in an ordered group iff \(S\) is cancellative.