A network of congruences on an ample semigroup (Q2031431)

In this paper, a network of congrunces on an ample semigroup is discussed. Ample semigroups are generalisations of inverse semigroups using generalised Green's relations: \(\mathcal{L}^*\) and \(\mathcal{R}^*\). The author discusses cancellative congruences, the semilattice congruences, the semilattice of cancellative monoids congruences, the strongly \(E\)-reflexive congruences and the \(E\)-unitary congruences on ample semigroups. The concept of \(P\)-congruence on an ample semigroup is introduced and the minimum admissible congruence is characterised for some special conditions based on a \(P\)-congruence. Also, some particular minimum admissible congruences on an ample semigroup are recognized and this is used to study a network of certain minimum admissible congruences on the semigroup.