(1) Mathematical Institute, University of St Andrews, Scotland;(2) Departamento de Matemática, F.C.T., Universidade Nova de Lisboa, Portugal
Abstract:
An ordered pair (e, f) of idempotents of a regular semigroup is called a skew pair
if ef is not idempotent whereas fe is idempotent. We have shown previously
that there are four distinct types of skew pairs of idempotents. Here we
consider the smallest regular semigroups that contain precisely one of each of
these four types. We show that, to within isomorphism and dualisomorphism,
there are six such semigroups and characterise them as quotient semigroups of
certain regular Rees matrix semigroups.