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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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.