Covering in the lattice of subuniverses of a finite distributive lattice

Abstract

The covering relation in the lattice of subuniverses of a finite distributive lattice 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.1991 Mathematics subject classification {Amer. Math. Soc): primary 06B05.