Varieties of K-lattices

Abstract

In this paper we deal with varieties of commutative residuated lattices that arise from a specific kind of construction: the twist-product of a lattice. Twist-products were first considered by Kalman in 1958 to deal with order involutions on plain lattices, but the extension of this concept to residuated lattices has attracted some attention lately. Here we deal mainly with varieties of such lattices that can be obtained by applying a specific twist-product construction to varieties of integral and commutative residuated lattices.