The structure of sublattices of the product of n lattices

Donald Mark Topkis

Vol. 65 (1976), No. 2, 525–532

DOI: 10.2140/pjm.1976.65.525

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.

Mathematical Subject Classification

Primary: 06A20, 06A20

Milestones

Received: 19 December 1975

Published: 1 August 1976