Lili Wang and Aifa Wang Chongqing University of Technology, Chongqing University of Technology
Abstract : In this paper, we give congruences on an abundant semigroup with a quasi-ideal $S$-adequate transversal $S^{\circ}$ by the congruence pair abstractly which consists of congruences on the structure component parts $R$ and $\Lambda$. We prove that the set of all congruences on this kind of semigroups is a complete lattice.
