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Congruence amalgamation of lattices

J. Tuma proved an interesting "congruence amalgamation" result. We are generalizing and providing an alternate proof for it. We then provide applications of this result: --A.P. Huhn proved that every distributive algebraic lattice $D$ with at most $\aleph\_1$ compact elements can be repres...

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Detalles Bibliográficos
Autores principales: Grätzer, G, Lakser, H, Wehrung, F
Lenguaje:eng
Publicado: 2005
Materias:
Acceso en línea:http://cds.cern.ch/record/853798
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author Grätzer, G
Lakser, H
Wehrung, F
author_facet Grätzer, G
Lakser, H
Wehrung, F
author_sort Grätzer, G
collection CERN
description J. Tuma proved an interesting "congruence amalgamation" result. We are generalizing and providing an alternate proof for it. We then provide applications of this result: --A.P. Huhn proved that every distributive algebraic lattice $D$ with at most $\aleph\_1$ compact elements can be represented as the congruence lattice of a lattice $L$. We show that $L$ can be constructed as a locally finite relatively complemented lattice with zero. --We find a large class of lattices, the $\omega$-congruence-finite lattices, that contains all locally finite countable lattices, in which every lattice has a relatively complemented congruence-preserving extension.
id cern-853798
institution Organización Europea para la Investigación Nuclear
language eng
publishDate 2005
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spelling cern-8537982019-09-30T06:29:59Zhttp://cds.cern.ch/record/853798engGrätzer, GLakser, HWehrung, FCongruence amalgamation of latticesMathematical Physics and MathematicsJ. Tuma proved an interesting "congruence amalgamation" result. We are generalizing and providing an alternate proof for it. We then provide applications of this result: --A.P. Huhn proved that every distributive algebraic lattice $D$ with at most $\aleph\_1$ compact elements can be represented as the congruence lattice of a lattice $L$. We show that $L$ can be constructed as a locally finite relatively complemented lattice with zero. --We find a large class of lattices, the $\omega$-congruence-finite lattices, that contains all locally finite countable lattices, in which every lattice has a relatively complemented congruence-preserving extension.math.GM/0501370oai:cds.cern.ch:8537982005-01-22
spellingShingle Mathematical Physics and Mathematics
Grätzer, G
Lakser, H
Wehrung, F
Congruence amalgamation of lattices
title Congruence amalgamation of lattices
title_full Congruence amalgamation of lattices
title_fullStr Congruence amalgamation of lattices
title_full_unstemmed Congruence amalgamation of lattices
title_short Congruence amalgamation of lattices
title_sort congruence amalgamation of lattices
topic Mathematical Physics and Mathematics
url http://cds.cern.ch/record/853798
work_keys_str_mv AT gratzerg congruenceamalgamationoflattices
AT lakserh congruenceamalgamationoflattices
AT wehrungf congruenceamalgamationoflattices