Varieties of bounded K-lattices

Abstract

In this paper we continue to study varieties of K-lattices, focusing on their bounded versions. These (bounded) commutative residuated lattices 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. We describe the lower part of the lattice of subvarieties of bounded K-lattices, showing that there is only one atom and describing up to a certain extent the covers of the atom. We also consider some special subvarieties of bounded K-lattices, and study the lattice of subvarieties for those cases.