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Abstract:

Given an integral commutative residuated lattice L, the product L × L can be endowed with the structure of a commutative residuated lattice with involution that we call a twist-product. In the present paper, we study the subvariety K of commutative residuated lattices that can be represented by twist-products. We give an equational characterization of K, a categorical interpretation of the relation among the algebraic categories of commutative integral residuated lattices and the elements in K, and we analyze the subvariety of representable algebras in K. Finally, we consider some specific class of bounded integral commutative residuated lattices G, and for each fixed element L ∈ G, we characterize the subalgebras of the twist-product whose negative cone is L in terms of some lattice filters of L, generalizing a result by Odintsov for generalized Heyting algebras. © 2014 Springer Basel.

Registro:

Documento: Artículo
Título:The subvariety of commutative residuated lattices represented by twist-products
Autor:Busaniche, M.; Cignoli, R.
Filiación:Instituto de Matemática Aplicada del Litoral- FIQ, CONICET-UNL, Guemes 3450, S3000GLN Santa Fe, Argentina
Departamento de Matemática, Universidad de Buenos Aires, Ciudad Universitaria, 1428 Buenos Aires, Argentina
Palabras clave:Glivenko residuated lattices; involution; residuated lattices; twist-products
Año:2014
Volumen:71
Número:1
Página de inicio:5
Página de fin:22
DOI: http://dx.doi.org/10.1007/s00012-014-0265-4
Título revista:Algebra Universalis
Título revista abreviado:Algebra Univers.
ISSN:00025240
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00025240_v71_n1_p5_Busaniche

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Citas:

---------- APA ----------
Busaniche, M. & Cignoli, R. (2014) . The subvariety of commutative residuated lattices represented by twist-products. Algebra Universalis, 71(1), 5-22.
http://dx.doi.org/10.1007/s00012-014-0265-4
---------- CHICAGO ----------
Busaniche, M., Cignoli, R. "The subvariety of commutative residuated lattices represented by twist-products" . Algebra Universalis 71, no. 1 (2014) : 5-22.
http://dx.doi.org/10.1007/s00012-014-0265-4
---------- MLA ----------
Busaniche, M., Cignoli, R. "The subvariety of commutative residuated lattices represented by twist-products" . Algebra Universalis, vol. 71, no. 1, 2014, pp. 5-22.
http://dx.doi.org/10.1007/s00012-014-0265-4
---------- VANCOUVER ----------
Busaniche, M., Cignoli, R. The subvariety of commutative residuated lattices represented by twist-products. Algebra Univers. 2014;71(1):5-22.
http://dx.doi.org/10.1007/s00012-014-0265-4