Free products of ordered semigroups
R. E. Johnson · Proceedings of the American Mathematical Society · 1968
Several years ago A. A. Vinogradov [1] proved that the free product of two ordered groups is orderable. In this note we give a simplified version of his proof, which also holds for semigroups. A semigroup S is said to be ordered iff it has a transitive linear ordering b1b2 in S1S2 iff either a1 > bi or a1 = b1 and a2> b2. The aim of this paper is to prove the following result.