Vol. 65, No. 2, 1976

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ISSN: 0030-8730
The structure of sublattices of the product of n lattices

Donald Mark Topkis

Vol. 65 (1976), No. 2, 525–532
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
Authors
Donald Mark Topkis