Covering in the lattice of subuniverses of a finite distributive lattice
Zsolt Lengvárszky, George F. McNulty · Journal of the Australian Mathematical Society Series A Pure Mathematics and Statistics · 1998
Abstract The covering relation in the lattice of subuniverses of a finite distributive lattices is characterized in terms of how new elements in a covering sublattice fit with the sublattice covered. In general, although the lattice of subuniverses of a finite distributive lattice will not be modular, nevertheless we are able to show that certain instances of Dedekind's Transposition Principle still hold. Weakly independent maps play a key role in our arguments.