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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/openAccess
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
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