Congruences on *-bisimple type A I-semigroups

Abstract

This paper studies congruences on a *-bisimple type A I-semigroup in the light of known results in the areas of inverse semigroups and type A ω-semigroups. It turns out that for a *-bisimple type A I-semigroup, we have the idempotent-separating congruence and the minimum cancellative monoid congruence.