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Representing a monotone map by principal lattice congruences

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Abstract

For a lattice L, let Princ (L) denote the ordered set of principal congruences of L. In a pioneering paper, G. Grätzer proved that bounded ordered sets (in other words, posets with 0 and 1) are, up to isomorphism, exactly the Princ (L) of bounded lattices L. Here we prove that for each 0-separating boundpreserving monotone map ψ between two bounded ordered sets, there are a lattice L and a sublattice K of L such that, in essence, ψ is the map from Princ (K) to Princ (L) that sends a principal congruence to the congruence it generates in the larger lattice.

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Authors and Affiliations

  1. Bolyai Institute, University of Szeged, Aradi vértanúk tere 1, Szeged, 6720, Hungary

    G. Czédli

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  1. G. Czédli
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Correspondence to G. Czédli.

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Dedicated to the memory of Gábor Szász

This research was supported by the European Union and co-funded by the European Social Fund under the project “Telemedicine-focused research activities on the field of Mathematics, Informatics and Medical sciences” of project number “TÁMOP-4.2.2.A-11/1/KONV-2012-0073”, and by NFSR of Hungary (OTKA), grant number K83219.

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Czédli, G. Representing a monotone map by principal lattice congruences. Acta Math. Hungar. 147, 12–18 (2015). https://doi.org/10.1007/s10474-015-0539-0

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  • DOI: https://doi.org/10.1007/s10474-015-0539-0

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