Periodica Mathematica Hungarica

, Volume 55, Issue 1, pp 61–79 | Cite as

Semilattice orders on the homomorphic images of the Rédei semigroup

  • Kamilla Kátai-UrbánEmail author
  • 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.

Key words and phrases

semilattice order principal ideal semigroup 

Mathematics subject classification number

20M99 06F05 


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Copyright information

© Springer Science+Business Media B.V. 2007

Authors and Affiliations

  1. 1.Bolyai InstituteUniversity of SzegedSzegedHungary

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