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dc.contributor.author Celani, Sergio Arturo
dc.contributor.author Esteban, María
dc.date.available 2018-09-10T17:41:15Z
dc.date.issued 2017-10
dc.identifier.citation Celani, Sergio Arturo; Esteban, María; Spectral-like duality for distributive Hilbert algebras with infimum; Springer; Algebra Universalis; 78; 2; 10-2017; 193-213
dc.identifier.issn 0002-5240
dc.identifier.uri http://hdl.handle.net/11336/58915
dc.description.abstract Distributive Hilbert algebras with infimum, or DH^-algebras for short, are algebras with implication and conjunction, in which the implication and the conjunction do not necessarily satisfy the residuation law. These algebras do not fall under the scope of the usual duality theory for lattice expansions, precisely because they lack residuation. We propose a new approach, that consists of regarding the conjunction as the additional operation on the underlying implicative structure. In this paper, we introduce a class of spaces, based on compactly-based sober topological spaces. We prove that the category of these spaces and certain relations is dually equivalent to the category of DH^-algebras and ∧ -semi-homomorphisms. We show that the restriction of this duality to a wide subcategory of spaces gives us a duality for the category of DH^-algebras and algebraic homomorphisms. This last duality generalizes the one given by the author in 2003 for implicative semilattices. Moreover, we use the duality to give a dual characterization of the main classes of filters for DH^-algebras, namely, (irreducible) meet filters, (irreducible) implicative filters and absorbent filters.
dc.format application/pdf
dc.language.iso eng
dc.publisher Springer
dc.rights info:eu-repo/semantics/restrictedAccess
dc.rights.uri https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.subject Hilbert algebras
dc.subject topological representation
dc.subject distributive semilattices
dc.subject.classification Matemática Pura
dc.subject.classification Matemáticas
dc.subject.classification CIENCIAS NATURALES Y EXACTAS
dc.title Spectral-like duality for distributive Hilbert algebras with infimum
dc.type info:eu-repo/semantics/article
dc.type info:ar-repo/semantics/artículo
dc.type info:eu-repo/semantics/publishedVersion
dc.date.updated 2018-09-10T13:19:07Z
dc.identifier.eissn 1420-8911
dc.journal.volume 78
dc.journal.number 2
dc.journal.pagination 193-213
dc.journal.pais Suiza
dc.description.fil Fil: Celani, Sergio Arturo. Universidad Nacional del Centro de la Provincia de Buenos Aires. Facultad de Ciencias Exactas. Núcleo Consolidado de Matemática Pura y Aplicada; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
dc.description.fil Fil: Esteban, María. Universidad Central de Barcelona; España
dc.journal.title Algebra Universalis
dc.relation.alternativeid info:eu-repo/semantics/altIdentifier/doi/http://dx.doi.org/10.1007/s00012-017-0451-2
dc.relation.alternativeid info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007%2Fs00012-017-0451-2
dc.conicet.fuente individual


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info:eu-repo/semantics/restrictedAccess Excepto donde se diga explícitamente, este item se publica bajo la siguiente descripción: Creative Commons Attribution-NonCommercial-ShareAlike 2.5 Unported (CC BY-NC-SA 2.5)