Semilattice orders on the homomorphic images of the Rédei semigroup |
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Authors: | Kamilla Kátai-Urbán Árpád Tritz |
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Institution: | (1) Bolyai Institute, University of Szeged, Aradi vértanúk tere 1, H-6720 Szeged, Hungary |
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Abstract: | The combinatorial simple principal ideal semigroups generated by two elements were described by L. Megyesi and G. Pollák.
The ‘most general’ among them is called the Rédei semigroup. The ‘most special’ combinatorial simple principal ideal semigroup
generated by two elements is the bicyclic semigroup. D. B. McAlister determined the compatible semilattice orders on the bicyclic
semigroup. Our aim is to study the compatible semilattice orders on the homomorphic images of the Rédei semigroup. We prove
that there are four compatible total orders on these semigroups. We show that on the Rédei semigroup, the total orders are
the only compatible semilattice orders. Moreover, on each proper homomorphic image of the Rédei semigroup, we give a compatible
semilattice order which is not a total order.
Communicated by Mária B. Szendrei |
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Keywords: | semilattice order principal ideal semigroup |
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