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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2014
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| 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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| Sumario: | 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. |
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