On the coset structure of distributive skew lattices

TL;DR

This paper explores the structure of distributive skew lattices, focusing on their coset structure and the independence of cancellation and distributivity properties, extending understanding beyond commutative cases.

Contribution

It reviews recent results on distributivity in skew lattices and provides new insights into their coset structures and combinatorial implications.

Findings

Distributivity and cancellation are independent in skew lattices.

The paper characterizes the coset structure of distributive skew lattices.

It discusses combinatorial implications of these algebraic properties.

Abstract

In the latest developments in the theory of skew lattices, distributivity has been one of the main topics of study. The largest classes of examples of such algebras are distributive. Unlike what happens in lattices, the properties of cancellation and distributivity are independent for skew lattices. In this paper we will discuss several aspects of distributivity in the absence of commutativity, review the recent results by Kinyon and Leech on these matters and have an insight on the coset structure of those algebras that satisfy this property. We will also discuss combinatorial implications of these results.