On the Least (Ordered) Semilattice Congruence in Ordered $\Gamma$-Semigroups

M. Siripitukdet, A. Iampan

Abstract

In this paper, we firstly characterize the relationship between the(ordered) filters, (ordered) s-prime ideals and (ordered) semilattice congruences in ordered $\Gamma$-semigroups. Finally, we give some characterizations of semilattice congruences and ordered semilattice congruences on ordered $\Gamma$-semigroups and prove that

1. n is the least semilattice congruence,

2. N is the least ordered semilattice congruence,

3. N is not the least semilattice congruence in general.