2013/07/31 by Joao Pita Costa
Mathematics · #math.RA #msc:06A11 #msc:06F05
published as Demonstratio Mathematica. Vol. XLVII No. 3, 2014, pp. 673-692 · 17 pages, submitted to Demonstratio Mathematica. arXiv admin note: text overlap with arXiv:1212.6495
arxiv created 2014/07/09 · arxiv updated 2014/07/10
Skew lattices are non-commutative generalizations of lattices. The coset structure decomposition is an original approach to the study of these algebras describing the relation between its rectangular classes. In this paper we will look at the category determined by these rectangular algebras and the morphisms between them, showing that not all skew lattices can determine such a category. Furthermore, we will present a class of examples of skew lattices in rings that are not strictly categorical, and present sufficient conditions for skew lattices of matrices in rings to constitute \wedge-distributive skew lattices.