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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| Dokumentumtípus: | Cikk |
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2015
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| 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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| 490 | 0 | |a ACTA MATHEMATICA HUNGARICA |v 147 No. 1 | |
| 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. | |
| 856 | 4 | 0 | |u http://publicatio.bibl.u-szeged.hu/14547/1/czedli_representing-a-monotone-map-by-principal-lattice-congruences.pdf |z Dokumentum-elérés |
| 856 | 4 | 0 | |u http://publicatio.bibl.u-szeged.hu/14547/7/actamathhung_047_001_content.pdf |z Dokumentum-elérés |