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 {Mathematical expression} of commutative residuated lattices that can be represented by twist-products. We give an equational characterization of {Mathematical expression}, a categorical interpretation of the relation among the algebraic categories of commutative integral residuated lattices and the elements in {Mathematical expression}, and we analyze the subvariety of representable algebras in {Mathematical expression}. Finally, we consider some specific class of bounded integral commutative residuated lattices {Mathematical expression}, and for each fixed element {Mathematical expression}, 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.
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, Santa Fe, S3000GLN, Argentina Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Buenos Aires, 1428, Argentina |
Idioma: | Inglés |
Palabras clave: | 2010 Mathematics Subject Classification: Primary: 03G10, Secondary: 03B47, 03G25 |
Año: | 2014 |
Página de inicio: | 1 |
Página de fin: | 18 |
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_v_n_p1_Busaniche |