The maximum idempotent-separating congruence on a regular semigroup
John C. Meakin · Proceedings of the Edinburgh Mathematical Society · 1972
It has been established by G. Lallement (3) that the set of idempotent-separating congruences on a regular semigroup S coincides with the set ∑( ) of congruences on S which are contained in Green's equivalence on S. In view of this and Lemma 10.3 of A. H. Clifford and G. B. Preston (1) it is obvious that the maximum idempotent-separating congruence on a regular semigroup S is given by