Classification of some τ-congruence-free completely regular semigroups

摘要

Let τ be an equivalence relation on a semigroup. We introduce τ-congruence-free semigroups, extending the notion of congruence-free semigroups, and classify all completely regular semigroups which are τ-congruence-free, where τ is one of Green's relations H, L and D respectively. Taking τ as H as well as D, this settles two open problems posed by M. Petrich and N. R. Reilly.