Rectangular products of lattices

✍ Scribed by M.K. Bennett

• Book ID: 103056195
• Publisher: Elsevier Science
• Year: 1990
• Tongue: English
• Weight: 934 KB
• Volume: 79
• Category: Article
• ISSN: 0012-365X
• DOI: 10.1016/0012-365x(90)90332-c

✦ Synopsis

If L, and L, are face lattices of convex polytopes, then L, 0 L, is the lattice of faces of the (topological) product of these polytopes. If L, and L, are concept lattices in the sense of Wille, then L, Cl L, is the concept lattice of the semiproduct of the underlying contexts.

In this article, properties which are preserved (or not preserved) by rectangular products are discussed, and necessary and sufficient conditions are given for a lattice to be a rectangular product.