Congruence lattices of free lattices in non-distributive varieties

We prove that for any free lattice F with at least $\aleph\_2$ generators in any non-distributive variety of lattices, there exists no sectionally complemented lattice L with congruence lattice isomorphic to the one of F. This solves a question formulated by Gr\"{a}tzer and Schmidt in 1962. Thi...

Descripción completa

Detalles Bibliográficos
Autores principales: Ploscica, M, Tuma, J, Wehrung, F
Lenguaje:eng
Publicado: 2005
Materias:
Mathematical Physics and Mathematics
Acceso en línea:http://cds.cern.ch/record/853819
_version_ 1780907024483090432
author Ploscica, M
Tuma, J
Wehrung, F
author_facet Ploscica, M
Tuma, J
Wehrung, F
author_sort Ploscica, M
collection CERN
description We prove that for any free lattice F with at least $\aleph\_2$ generators in any non-distributive variety of lattices, there exists no sectionally complemented lattice L with congruence lattice isomorphic to the one of F. This solves a question formulated by Gr\"{a}tzer and Schmidt in 1962. This yields in turn further examples of simply constructed distributive semilattices that are not isomorphic to the semilattice of finitely generated two-sided ideals in any von Neumann regular ring.
id cern-853819
institution Organización Europea para la Investigación Nuclear
language eng
publishDate 2005
record_format invenio
spelling cern-8538192019-09-30T06:29:59Zhttp://cds.cern.ch/record/853819engPloscica, MTuma, JWehrung, FCongruence lattices of free lattices in non-distributive varietiesMathematical Physics and MathematicsWe prove that for any free lattice F with at least $\aleph\_2$ generators in any non-distributive variety of lattices, there exists no sectionally complemented lattice L with congruence lattice isomorphic to the one of F. This solves a question formulated by Gr\"{a}tzer and Schmidt in 1962. This yields in turn further examples of simply constructed distributive semilattices that are not isomorphic to the semilattice of finitely generated two-sided ideals in any von Neumann regular ring.math.GM/0501459oai:cds.cern.ch:8538192005-01-25
spellingShingle Mathematical Physics and Mathematics
Ploscica, M
Tuma, J
Wehrung, F
Congruence lattices of free lattices in non-distributive varieties
title Congruence lattices of free lattices in non-distributive varieties
title_full Congruence lattices of free lattices in non-distributive varieties
title_fullStr Congruence lattices of free lattices in non-distributive varieties
title_full_unstemmed Congruence lattices of free lattices in non-distributive varieties
title_short Congruence lattices of free lattices in non-distributive varieties
title_sort congruence lattices of free lattices in non-distributive varieties
topic Mathematical Physics and Mathematics
url http://cds.cern.ch/record/853819
work_keys_str_mv AT ploscicam congruencelatticesoffreelatticesinnondistributivevarieties
AT tumaj congruencelatticesoffreelatticesinnondistributivevarieties
AT wehrungf congruencelatticesoffreelatticesinnondistributivevarieties

Ejemplares similares