distributive lattice

A latticeMathworldPlanetmath (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(yz)=(xy)(xz)

  • x(yz)=(xy)(xz)

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

Examples of distributive lattices include Boolean lattices (http://planetmath.org/BooleanLattice), totally ordered setsMathworldPlanetmath, and the subgroupMathworldPlanetmathPlanetmath 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