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In this paper, we give congruences on an abundant semigroup with a quasi-ideal S-adequate transversal S◦ by the congruence pair abstractly which consists of congruences on the structure component parts R and Λ. We prove that the set of all congruences on this kind of semigroups is a complete lattice.

CONGRUENCES ON ABUNDANT SEMIGROUPS WITH QUASI-IDEAL S-ADEQUATE TRANSVERSALS