Prime spectra of lattice-ordered abelian groups
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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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 |
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Universidad de Buenos Aires |
institution_str |
I-28 |
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R-134 |
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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 |
_version_ |
1807320313311002624 |