Inverse transversal congruence extensions
M. H. Almeida Santos · Communications in Algebra · 1998
If S is a regular semigroup then an inverse transversal of S is an inverse H bsemigroup S° that contains precisely one inverse x° of each x ε S. Here we describe, for every congruence π on S° that can be extended to S, the smallest extension of π. We also describe the idempotent separating congruences on S.