CONICET | Buscador de Institutos y Recursos Humanos

Given an integral commutative residuated lattice L, the productL × L can be endowed with an structure of commutative residuated latticewith involution, that we call twist-product. In the present paper we studythe subvariety K of commutative residuated lattices that can be representedby twist-products. We give an equational characterization of K, a categoricalinterpretation of the relation among the algebraic categories of commutativeintegral 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 in 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.