Congruences on abundant semigroups with quasi-ideal $S$-adequate transversals
Commun. Korean Math. Soc. 2014 Vol. 29, No. 1, 1-8
Printed January 31, 2014
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.
Keywords : abundant semigroup, adequate transversal, quasi-ideal transversal, congruence, congruence pair
MSC numbers : 20M10
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