The structure of sublattices of the product of<i>n</i>lattices

Abstract

The structure of sublattices of the product of n lattices is explored. Such a sublattice is decomposed and completely characterized in terms of n(n-1)/2 sublattices of the product of two lattices. A sublattice of the product of two lattices is represented in terms of several easily characterized sublattices. The sublattice characterizations provide analogous characterizations for those functions whose level sets are sublattices. A simple representation is also given for the sections of a sublattice of the product of two lattices.