Data de publicação: Dec 30, 2019 9:12:12 AM

A new paper was released yesterday providing a view on the coset structure of distributive skew lattices. This is a result from the collaboration reestablished at the Non-commutative structures Workshop that happened in the summer of 2018. It is published within a special edition of the ADAM math journal dedicated to Skew Lattices, including a section of open problems proposed by the participants of the workshop.

On the coset structure of distributive skew lattices

The Art of Discrete and Applied Mathematics, Vol 2 No 2 (2019)

https://adam-journal.eu/index.php/ADAM/article/view/1305

João Pita Costa

Jožef Stefan Institute, Slovenia

https://orcid.org/0000-0001-5745-1302

Jonathan Leech

Westmont College, United States

DOI: https://doi.org/10.26493/2590-9770.1305.f45

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.

Keywords: Skew lattices, distributive structures, noncommutative structures, ordered structures, bands of semigroups