The subvariety of commutative residuated lattices represented by twist-products

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 ca...

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Autor principal: Busaniche, Manuela
Publicado: 2014
Materias:
2010 Mathematics Subject Classification: Primary: 03G10, Secondary: 03B47, 03G25
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00025240_v_n_p1_Busaniche
http://hdl.handle.net/20.500.12110/paper_00025240_v_n_p1_Busaniche
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
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spelling paper:paper_00025240_v_n_p1_Busaniche2023-06-08T14:21:53Z The subvariety of commutative residuated lattices represented by twist-products Busaniche, Manuela 2010 Mathematics Subject Classification: Primary: 03G10, Secondary: 03B47, 03G25 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. Fil:Busaniche, M. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2014 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00025240_v_n_p1_Busaniche http://hdl.handle.net/20.500.12110/paper_00025240_v_n_p1_Busaniche
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic 2010 Mathematics Subject Classification: Primary: 03G10, Secondary: 03B47, 03G25
spellingShingle 2010 Mathematics Subject Classification: Primary: 03G10, Secondary: 03B47, 03G25
Busaniche, Manuela
The subvariety of commutative residuated lattices represented by twist-products
topic_facet 2010 Mathematics Subject Classification: Primary: 03G10, Secondary: 03B47, 03G25
description 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.
author Busaniche, Manuela
author_facet Busaniche, Manuela
author_sort Busaniche, Manuela
title The subvariety of commutative residuated lattices represented by twist-products
title_short The subvariety of commutative residuated lattices represented by twist-products
title_full The subvariety of commutative residuated lattices represented by twist-products
title_fullStr The subvariety of commutative residuated lattices represented by twist-products
title_full_unstemmed The subvariety of commutative residuated lattices represented by twist-products
title_sort subvariety of commutative residuated lattices represented by twist-products
publishDate 2014
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00025240_v_n_p1_Busaniche
http://hdl.handle.net/20.500.12110/paper_00025240_v_n_p1_Busaniche
work_keys_str_mv AT busanichemanuela thesubvarietyofcommutativeresiduatedlatticesrepresentedbytwistproducts
AT busanichemanuela subvarietyofcommutativeresiduatedlatticesrepresentedbytwistproducts
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