Tensor Extensions
Birkhäuser Boston eBooks · 2007
Let A and B be nontrivial finite lattices. Then ConA × ConB is a finite distributive lattice, so by the Dilworth Theorem (Theorem 7.1), the lattice ConA × ConB can be represented as ConL, for some finite lattice L. How can we construct the lattice L from the lattices A and B? By Theorem 2.1, (1) $$ Con(A \times B) \cong ConA \times ConB, $$ so we can take L = A × B.