A new paper on skew lattices out now

Data de publicação: Aug 20, 2012 10:7:19 AM

The author thanks Fundação para a Ciência e Tecnologia, ref. SFRH/BD/36694/2007 for support.

Presented by M. Jackson.

Keywords and phrases noncommutative lattice – skew lattice – symmetric – categorical – cancellative – distributive – coset structure – index

2010 Mathematics Subject Classification Primary: 06A11 – Secondary: 06F05 – 06B75

During the last three decades, skew lattices proved to be the most successful noncommutative generalization of lattices. In recent times, the study of categorical skew lattices has revealed its importance, especially in the context of several recent investigations of distributivity and cancellation for skew lattices. In this work, we present several characterizations for categorical skew lattices, as well as the description of its coset structure through the study of coset bijections. Several relevant combinatorial results are consequences of this characterization.

Abstract

Dear skew community,

it is my pleasure to announce the new paper on categorical skew lattices:

Coset Laws for Categorical Skew Lattices. Algebra Universalis. DOI: 10.1007/s00012-012-0194-z

this paper discusses the coset structure of categorical skew lattices and presents several equivalent perspectives on how to approach such a variety of algebras. It is an important part of my Ph. D. dissertation as it consists on a significant contribution to the study of distributivity in non commutative lattices.