Distributivity in Lattices

A lattice L is infinitely (join) distributive if a ∩ ∪ B b = ∪ B ( a ∩ b ) whenever the indicated joins exist in L . Clearly infinite distributivity implies ordinary distributivity. On the other hand it is easy to give examples of distributive lattices which are not infinitely distributive. For example, the rational integers under the relation of division form a distributive lattice which is not infinitely distributive. However for complemented lattices, as observed by Tarski [8] and von Neumann [6], distributivity implies infinite distributivity. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.