Abstract:
We follow the ideas given by Chen and Grätzer to represent Stone algebras and adapt them for the case of Stonean residuated lattices. Given a Stonean residuated lattice, we consider the triple formed by its Boolean skeleton, its algebra of dense elements and a connecting map. We define a category whose objects are these triples and suitably defined morphisms, and prove that we have a categorical equivalence between this category and that of Stonean residuated lattices. We compare our results with other works and show some applications of the equivalence. © 2018, Springer Science+Business Media B.V., part of Springer Nature.
Registro:
Documento: |
Artículo
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Título: | A Categorical Equivalence for Stonean Residuated Lattices |
Autor: | Busaniche, M.; Cignoli, R.; Marcos, M.A. |
Filiación: | Instituto de Matemática Aplicada del Litoral, UNL, CONICET, FIQ, Predio Dr. Alberto Cassano del CCT-CONICET-Santa Fe, Colectora de la Ruta Nacional no. 168, Santa Fe, Argentina Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Buenos Aires, 1428, Argentina
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Palabras clave: | Boolean algebras; Stonean residuated lattices; Triples |
Año: | 2019
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Volumen: | 107
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Número: | 2
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Página de inicio: | 399
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Página de fin: | 421
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DOI: |
http://dx.doi.org/10.1007/s11225-018-9800-1 |
Título revista: | Studia Logica
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Título revista abreviado: | Stud. Logica
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ISSN: | 00393215
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Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00393215_v107_n2_p399_Busaniche |
Referencias:
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Citas:
---------- APA ----------
Busaniche, M., Cignoli, R. & Marcos, M.A.
(2019)
. A Categorical Equivalence for Stonean Residuated Lattices. Studia Logica, 107(2), 399-421.
http://dx.doi.org/10.1007/s11225-018-9800-1---------- CHICAGO ----------
Busaniche, M., Cignoli, R., Marcos, M.A.
"A Categorical Equivalence for Stonean Residuated Lattices"
. Studia Logica 107, no. 2
(2019) : 399-421.
http://dx.doi.org/10.1007/s11225-018-9800-1---------- MLA ----------
Busaniche, M., Cignoli, R., Marcos, M.A.
"A Categorical Equivalence for Stonean Residuated Lattices"
. Studia Logica, vol. 107, no. 2, 2019, pp. 399-421.
http://dx.doi.org/10.1007/s11225-018-9800-1---------- VANCOUVER ----------
Busaniche, M., Cignoli, R., Marcos, M.A. A Categorical Equivalence for Stonean Residuated Lattices. Stud. Logica. 2019;107(2):399-421.
http://dx.doi.org/10.1007/s11225-018-9800-1