The structure of sublattices of the product of n lattices
Donald M. Topkis · Pacific Journal of Mathematics · 1976
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.