The aim of this paper is to study the congruences on abundant semigroups with quasi-ideal adequate transversals. The good congruences on an abundant semigroup with a quasi-ideal adequate transversal S° are described by the equivalence triple abstractly which consists of equivalences on the structure component parts I, S° and Λ. Also, it is shown that the set of all good congruences on this kind of semigroup forms a complete lattice.
Blyth, T. S. and McFadden, R. B.Regular semigroups with a multiplicative inverse transversal, Proc. Roy. Soc. Edinburgh, 92A (1982), 253–270.
Blyth, T. S. and McFadden, R. B.Regular semigroups with a multiplicative inverse transversal, Proc. Roy. Soc. Edinburgh, 92A (1982), 253–270.)| false
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Studia Scientiarum Mathematicarum Hungarica
2021 Volume 58
Magyar Tudományos Akadémia
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