Representing a monotone map by principal lattice congruences

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...

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Elmentve itt :
Bibliográfiai részletek
Szerző: Czédli Gábor
Dokumentumtípus: Cikk
Megjelent: 2015
Sorozat:ACTA MATHEMATICA HUNGARICA 147 No. 1
doi:10.1007/s10474-015-0539-0

mtmt:2984003
Online Access:http://publicatio.bibl.u-szeged.hu/14547
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520 3 |a 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. © 2015, Akadémiai Kiadó, Budapest, Hungary. 
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