PRODUCTS OF SKELETONS OF FINITE DISTRIBUTIVE LATTICES
Joanna Grygiel · 2011
We prove that the skeleton of a product of nitely many nite distributive lattices is isomorphic to the product of skeletons of its factors. Thus, it is possible to construct nite distributive lattices with a given directly reducible skeleton by reducing the problem to the skeleton factors. Although not all possible lattices can be obtained this way, we show that it works for the smallest distributive lattice with the skeleton being a product of H-irreducible lattices.