Definition:Distributive Lattice

Definition
Let $\struct {S, \vee, \wedge, \preceq}$ be a lattice.

Then $\struct {S, \vee, \wedge, \preceq}$ is distributive one of the following statements holds:

That these statements are in fact equivalent is shown on Equivalence of Definitions of Distributive Lattice.

Hence, $\struct {S, \vee, \wedge, \preceq}$ is distributive $\wedge$ and $\vee$ distribute over each other.

Also see

 * Equivalence of Definitions of Distributive Lattice