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Commun. Korean Math. Soc. 2014; 29(1): 1-8
Printed January 31, 2014
https://doi.org/10.4134/CKMS.2014.29.1.1
Copyright © The Korean Mathematical Society.
Congruences on abundant semigroups with quasi-ideal $S$-adequate transversals
Lili Wang and Aifa Wang
Chongqing University of Technology, Chongqing University of Technology
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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