Principal right congruences on completely 0-simple semigroups

Abstract

In this paper principal right congruences on completely 0-simple semigroups are identified which consequently leads to identifying principal right congruences on classes of semigroups namely, Brandt semigroups, right groups, left groups, right zero semigroups, left zero semigroups and rectangular bands. As a consequence of this characterization, we show that the class of right subdirectly irreducible completely 0-simple semigroups with more than 3 elements is that of cocyclic 0-groups. Moreover, we prove that right irreducible completely 0-simple semigroups with more than 3 elements are 0-groups for which nontrivial subgroups have nontrivial intersections.