2012/12/28 by João Pita Costa, Joao Pita Costa, Costa, Joao Pita · 1 citation
Computer Science · Mathematics · #Advanced Algebra and Logic #FOS: Mathematics #Rings and Algebras (math.RA) #Rough Sets and Fuzzy Logic #math.RA #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1212.6495
This paper has been withdrawn by the author due to many of its ideas being published in the paper "Distributive Skew Lattices"
openalex publication_date 2012/12/28 · arxiv created 2013/07/05 · arxiv updated 2013/07/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.