The subvariety of commutative residuated lattices represented by twist-products

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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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Autores principales:	Busaniche, M., Cignoli, R.
Formato:	INPR
Lenguaje:	English
Materias:	2010 Mathematics Subject Classification: Primary: 03G10, Secondary: 03B47, 03G25
Acceso en línea:	http://hdl.handle.net/20.500.12110/paper_00025240_v_n_p1_Busaniche
Aporte de:	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires

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spelling	todo:paper_00025240_v_n_p1_Busaniche2023-10-03T13:52:28Z The subvariety of commutative residuated lattices represented by twist-products Busaniche, M. Cignoli, R. 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. INPR English info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar 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)
language	English
orig_language_str_mv	English
topic	2010 Mathematics Subject Classification: Primary: 03G10, Secondary: 03B47, 03G25
spellingShingle	2010 Mathematics Subject Classification: Primary: 03G10, Secondary: 03B47, 03G25 Busaniche, M. Cignoli, R. 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.
format	INPR
author	Busaniche, M. Cignoli, R.
author_facet	Busaniche, M. Cignoli, R.
author_sort	Busaniche, M.
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
url	http://hdl.handle.net/20.500.12110/paper_00025240_v_n_p1_Busaniche
work_keys_str_mv	AT busanichem thesubvarietyofcommutativeresiduatedlatticesrepresentedbytwistproducts AT cignolir thesubvarietyofcommutativeresiduatedlatticesrepresentedbytwistproducts AT busanichem subvarietyofcommutativeresiduatedlatticesrepresentedbytwistproducts AT cignolir subvarietyofcommutativeresiduatedlatticesrepresentedbytwistproducts
_version_	1782027119153381376

The subvariety of commutative residuated lattices represented by twist-products

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