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):

•
$x\\land(y\\lor z)=(x\\land y)\\lor(x\\land z)$
•
$x\\lor(y\\land z)=(x\\lor y)\\land(x\\lor z)$

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.

单词	DistributiveLattice
释义	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): • $x\\land(y\\lor z)=(x\\land y)\\lor(x\\land z)$ • $x\\lor(y\\land z)=(x\\lor y)\\land(x\\lor z)$ 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.
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