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):

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

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$x\vee (y\wedge z)=(x\vee y)\wedge (x\vee z)$
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  20130322 12:27:23 
Last modified on  20130322 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 