distributive lattice

A lattice (http://planetmath.org/Lattice) is said to be distributive if it satisifes either (and therefore both) of the distributive laws (http://planetmath.org/Distributive):

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

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

Every distributive lattice is modular (http://planetmath.org/ModularLattice).

Examples of distributive lattices include Boolean lattices (http://planetmath.org/BooleanLattice), totally ordered sets, and the subgroup lattices (http://planetmath.org/LatticeOfSubgroups) of locally cyclic groups.

Title	distributive lattice
Canonical name	DistributiveLattice
Date of creation	2013-03-22 12:27:23
Last modified on	2013-03-22 12:27:23
Owner	yark (2760)
Last modified by	yark (2760)
Numerical id	20
Author	yark (2760)
Entry type	Definition
Classification	msc 06D99
Related topic	Distributive
Related topic	Lattice
Related topic	BirkhoffPrimeIdealTheorem