Distributive Lattice

A Lattice which satisfies the identities

$$(x\wedge y)\vee(x\wedge z)=x\wedge(y\vee z)$$

$$(x\vee y)\wedge(x\vee z)=x\vee(y\wedge z)$$

is said to be distributive.

See also Lattice, Modular Lattice

References

Grätzer, G. Lattice Theory: First Concepts and Distributive Lattices. San Francisco, CA: W. H. Freeman, pp. 35-36, 1971.