Projective distributive lattices
Raymond Balbes, Alfred Horn · Pacific Journal of Mathematics · 1970
It will be shown that a countable distributive lattice is protective if and only if the product of any two join irreducible elements is join irreducible, and every element of the lattice is both a finite sum of join irreducible elements and a finite product of meet irreducible elements.For an arbitrary distributive lattice, necessary and sufficient conditions for projectivity are obtained by adding to these conditions a further condition on the set of join irreducible elements.