Rectangular products of lattices
The author discusses the properties which are preserved or not preserved in rectangular products \(L_ 1\square L_ 2\) of given lattices \(L_ 1\) and \(L_ 2\). If \(L_ 1\) and \(L_ 2\) are face lattices then \(L_ 1\square L_ 2\) is the lattice of faces of the (topological) product of these polytopes. If \(L_ 1\) and \(L_ 2\) are concept lattices in the sense of Wille, then \(L_ 1\square L_ 2\) is the concept lattice of the semiproduct of the underlying contexts. The author gives necessary and sufficient conditions for a lattice to be a rectangular product.
scientific article; zbMATH DE number 4134109