Varieties of Bounded K-lattices

TL;DR

This paper explores the properties and classifications of bounded K-lattices, a special class of residuated lattices constructed via twist-products, extending classical lattice theory with new insights.

Contribution

It advances the understanding of bounded K-lattices by analyzing their structure and varieties, building on the concept of twist-products in residuated lattice theory.

Findings

Characterization of bounded K-lattices

Extension of twist-product construction to residuated lattices

New classifications of lattice varieties

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 {\em 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.