caa a22 4500 463171489 CHVBK 20180406164814.0 cr unu---uuuuu 170326e20070901xx s 000 0 eng 10.1007/s10998-007-3061-x doi (NATIONALLICENCE)springer-10.1007/s10998-007-3061-x Semilattice orders on the homomorphic images of the Rédei semigroup [Elektronische Daten] [Kamilla Kátai-Urbán, Árpád Tritz] 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. Springer Science+Business Media B.V., 2007 semilattice order nationallicence principal ideal semigroup nationallicence Kátai-Urbán Kamilla Bolyai Institute, University of Szeged, Aradi vértanúk tere 1, H-6720, Szeged, Hungary aut Tritz Árpád Bolyai Institute, University of Szeged, Aradi vértanúk tere 1, H-6720, Szeged, Hungary aut Periodica Mathematica Hungarica Springer Netherlands 55/1(2007-09-01), 61-79 0031-5303 55:1<61 2007 55 10998 https://doi.org/10.1007/s10998-007-3061-x text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10998-007-3061-x text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Kátai-Urbán Kamilla Bolyai Institute, University of Szeged, Aradi vértanúk tere 1, H-6720, Szeged, Hungary aut NATIONALLICENCE 700 1- Tritz Árpád Bolyai Institute, University of Szeged, Aradi vértanúk tere 1, H-6720, Szeged, Hungary aut NATIONALLICENCE 773 0- Periodica Mathematica Hungarica Springer Netherlands 55/1(2007-09-01), 61-79 0031-5303 55:1<61 2007 55 10998 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer