A NOTE ON PSEUDOVARIETIES OF COMPLETELY REGULAR SEMIGROUPS

Abstract

A paper of Almeida and Trotter [‘The pseudoidentity problem and reducibility for completely regular semigroups’, Bull. Aust. Math. Soc.63 (2001), 407–433] makes essential use of free profinite semigroupoids over profinite graphs with infinitely many vertices. It has since been shown that such structures must be handled with great care. In this note, it is verified that the required properties hold for the profinite graphs considered by Almeida and Trotter, thereby filling the gaps in the proof.