A lattice is said to be distributive if it satisifes either (and therefore both) of the distributive laws:

• $x \land (y \lor z) = (x \land y) \lor (x \land z)$
• $x \lor (y \land z) = (x \lor y) \land (x \lor z)$

Examples of distributive lattices include Boolean lattices, totally ordered sets, and the subgroup lattices of locally cyclic groups.