What is "distributive lattice"

n. (context algebra English) A lattice in which the "meet" and the "join" operations are distributive with respect to each other.

In mathematics, a distributive lattice is a lattice in which the operations of join and meet distribute over each other. The prototypical examples of such structures are collections of sets for which the lattice operations can be given by set union and intersection. Indeed, these lattices of sets describe the scenery completely: every distributive lattice is – up to isomorphism – given as such a lattice of sets.