A note on pseudocongruences in semigroups

In [1] we introduced the concept of pseudoorder in ordered semigroups and we proved that each pseudoorder on an ordered semigroup $S$ induces a congruence $\sigma$ on $S$ such that $S/\sigma$ is an ordered semigroup. In this short note we introduce the concept of pseudocongruence in semigroups and we prove that each pseudocongruence on a semigroup $S$ induces a congruence $\sigma$ on $S$ such that $S/\sigma$ is an ordered semigroup.