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Homedistributive lattice
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distributive lattice
A lattice is said to be distributive if it satisifes either (and therefore both) of the distributive laws:

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

$x\lor(y\land z)=(x\lor y)\land(x\lor z)$
Every distributive lattice is modular.
Examples of distributive lattices include Boolean lattices, totally ordered sets, and the subgroup lattices of locally cyclic groups.
Related:
Distributive, Lattice, BirkhoffPrimeIdealTheorem
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