On the coset structure of distributive skew lattices

Abstract

In the latest developments in the theory of skew lattices, the study of distributivity has been one of the main topics. The largest classes of examples of skew lattices thus far encountered are distributive. In this paper, we will discuss several aspects of distributivity in the absence of commutativity, and review recent related results in the context of the coset structure of skew lattices. We show that the coset perspective is essential to fully understand the nature of skew lattices and distributivity in particular. We will also discuss the combinatorial implications of these results and their impact in the study of skew lattices.