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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Detalles Bibliográficos
Autores principales: Cignoli, R., Gluschankof, D., Lucas, F.
Formato: Artículo publishedVersion
Lenguaje:Inglés
Publicado: 1999
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_00224049_v136_n3_p217_Cignoli
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Sumario: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.