On the coset structure of a skew lattice
arXiv:1302.3519
Abstract
The class of skew lattices can be seen as an algebraic category. It models an algebraic theory in the category of Sets where the Green's relation D is a congruence describing an adjunction to the category of Lattices. In this paper we will discuss the relevance of this approach, revisit some known decompositions and relate the order structure of a skew lattice with its coset structure that describes the internal coset decomposition of the respective algebra.
Demonstratio Mathematica Vol. XLIV No. 4 (2011)