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 K of commutative residuated lattices that can be represented by twis...
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| Formato: | JOUR |
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_00025240_v71_n1_p5_Busaniche |
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todo:paper_00025240_v71_n1_p5_Busaniche2023-10-03T13:52:27Z The subvariety of commutative residuated lattices represented by twist-products Busaniche, M. Cignoli, R. Glivenko residuated lattices involution residuated lattices 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 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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_00025240_v71_n1_p5_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 |
Glivenko residuated lattices involution residuated lattices twist-products |
| spellingShingle |
Glivenko residuated lattices involution residuated lattices twist-products Busaniche, M. Cignoli, R. The subvariety of commutative residuated lattices represented by twist-products |
| topic_facet |
Glivenko residuated lattices involution residuated lattices twist-products |
| 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 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. |
| format |
JOUR |
| 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_v71_n1_p5_Busaniche |
| work_keys_str_mv |
AT busanichem thesubvarietyofcommutativeresiduatedlatticesrepresentedbytwistproducts AT cignolir thesubvarietyofcommutativeresiduatedlatticesrepresentedbytwistproducts AT busanichem subvarietyofcommutativeresiduatedlatticesrepresentedbytwistproducts AT cignolir subvarietyofcommutativeresiduatedlatticesrepresentedbytwistproducts |
| _version_ |
1782027320445370368 |