Prime spectra of lattice-ordered abelian groups

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We prove that for each ℓ-group G, the topological space Spec(G) satisfies a condition Idω. Generalising a previous construction of Delzell and Madden we show that for each nondenumerable cardinal there is a completely normal spectral space that is not homeomorphic to Spec(G) for any ℓ-group G. We sh...

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Detalles Bibliográficos
Autores principales: Cignoli, R., Gluschankof, D., Lucas, F.
Formato: Artículo publishedVersion
Publicado: 1999
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_00224049_v136_n3_p217_Cignoli
https://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_00224049_v136_n3_p217_Cignoli_oai
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Repositorio Digital de la Universidad de Buenos Aires (UBA) de Universidad de Buenos Aires
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spelling I28-R145-paper_00224049_v136_n3_p217_Cignoli_oai2024-08-16 Cignoli, R. Gluschankof, D. Lucas, F. 1999 We prove that for each ℓ-group G, the topological space Spec(G) satisfies a condition Idω. Generalising a previous construction of Delzell and Madden we show that for each nondenumerable cardinal there is a completely normal spectral space that is not homeomorphic to Spec(G) for any ℓ-group G. We show also that a stronger form of property Idω, called Id, suffices to ensure that a completely normal spectral space is homeomorphic to Spec(G) for some ℓ-group G. © 1999 Elsevier Science B.V. All rights reserved. Fil:Gluschankof, D. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. application/pdf http://hdl.handle.net/20.500.12110/paper_00224049_v136_n3_p217_Cignoli info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar J. Pure Appl. Algebra 1999;136(3):217-229 Prime spectra of lattice-ordered abelian groups info:eu-repo/semantics/article info:ar-repo/semantics/artículo info:eu-repo/semantics/publishedVersion https://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_00224049_v136_n3_p217_Cignoli_oai
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-145
collection Repositorio Digital de la Universidad de Buenos Aires (UBA)
description We prove that for each ℓ-group G, the topological space Spec(G) satisfies a condition Idω. Generalising a previous construction of Delzell and Madden we show that for each nondenumerable cardinal there is a completely normal spectral space that is not homeomorphic to Spec(G) for any ℓ-group G. We show also that a stronger form of property Idω, called Id, suffices to ensure that a completely normal spectral space is homeomorphic to Spec(G) for some ℓ-group G. © 1999 Elsevier Science B.V. All rights reserved.
format Artículo
Artículo
publishedVersion
author Cignoli, R.
Gluschankof, D.
Lucas, F.
spellingShingle Cignoli, R.
Gluschankof, D.
Lucas, F.
Prime spectra of lattice-ordered abelian groups
author_facet Cignoli, R.
Gluschankof, D.
Lucas, F.
author_sort Cignoli, R.
title Prime spectra of lattice-ordered abelian groups
title_short Prime spectra of lattice-ordered abelian groups
title_full Prime spectra of lattice-ordered abelian groups
title_fullStr Prime spectra of lattice-ordered abelian groups
title_full_unstemmed Prime spectra of lattice-ordered abelian groups
title_sort prime spectra of lattice-ordered abelian groups
publishDate 1999
url http://hdl.handle.net/20.500.12110/paper_00224049_v136_n3_p217_Cignoli
https://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_00224049_v136_n3_p217_Cignoli_oai
work_keys_str_mv AT cignolir primespectraoflatticeorderedabeliangroups
AT gluschankofd primespectraoflatticeorderedabeliangroups
AT lucasf primespectraoflatticeorderedabeliangroups
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