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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Autores principales: Cignoli, R., Gluschankof, D., Lucas, F.
Formato: JOUR
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_00224049_v136_n3_p217_Cignoli
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
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spelling todo:paper_00224049_v136_n3_p217_Cignoli2023-10-03T14:32:37Z Prime spectra of lattice-ordered abelian groups Cignoli, R. Gluschankof, D. Lucas, F. 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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_00224049_v136_n3_p217_Cignoli
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (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 JOUR
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
url http://hdl.handle.net/20.500.12110/paper_00224049_v136_n3_p217_Cignoli
work_keys_str_mv AT cignolir primespectraoflatticeorderedabeliangroups
AT gluschankofd primespectraoflatticeorderedabeliangroups
AT lucasf primespectraoflatticeorderedabeliangroups
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