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Acta Mathematica Hungarica

, Volume 147, Issue 1, pp 12–18 | Cite as

Representing a monotone map by principal lattice congruences

  • G. Czédli
Article

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.

Key words and phrases

principal congruence lattice congruence ordered set order poset quasi-colored lattice preordering quasiordering monotone map 

Mathematics Subject Classification

06B10 

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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2015

Authors and Affiliations

  1. 1.Bolyai InstituteUniversity of SzegedSzegedHungary

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