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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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 |
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Universidad de Buenos Aires |
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I-28 |
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R-145 |
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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 |
_version_ |
1809356793829130240 |