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The semilattice congruences play an important role in studying the decomposition of semigroups -without order. When we pass from semigroups without order to ordered semigroups, the same role is played by the complete semilattice congruences. So, the complete semilattice congruences play an essential role in studying the structure, especially the decomposition of ordered semigroups. The characterization of complete semilattices of semigroups of a given type has been already considered by thedoi:10.12988/imf.2007.07102 fatcat:2pyeuk63jzhqvps6n54wurvptm