Internal decompositions of skew lattices Karin Cvetko-Vah * December 13, 2005 Abstract In the present note we study internal decompositions of skew lat- tices. This provides further insight into the structure of skew lattices. Special attention is devoted to skew lattices in rings. Math. Subj. Class. 2000: 06A06, 20M17, 20M25 Keywords: semigroup, band, skew lattice. * Karin Cvetko-Vah, Department of Mathematics, Faculty for Mathematics and Physics, University of Ljubljana, Jadranska 19, 1000 Ljubljana, Slovenia, E-mail address: karin.cvetko@fmf.uni-lj.si 1