Abstract

Congruences on inverse semigroups via the (kernel-trace) method introduced by Scheiblich in 1974. In this paper we discuss the congruences on inverse semigroups by using the technique of Kernel normal systems. Congrueneses on inverse semigroup were described in terms of congruences pairs (ker tr ). It is natural to ask if this strategy can be extended to include regular semigroups. Feigenbaum in 1979 has achieved this. However, this approach has not proved to be the best possible for congruences on regular semigroups in general. Whilst it is possible to describe abstractly the trace and kernel of congruence on a regular semigroup, these descriptions are unwieldy. The technique which has proved most useful for studying congruences on arbitrary regular semigroups is that due to Preston of Kernel normal systems.