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Distributive Lattice

A Lattice which satisfies the identities

\begin{displaymath}
(x\wedge y)\vee(x\wedge z)=x\wedge(y\vee z)
\end{displaymath}


\begin{displaymath}
(x\vee y)\wedge(x\vee z)=x\vee(y\wedge z)
\end{displaymath}

is said to be distributive.

See also Lattice, Modular Lattice


References

Grätzer, G. Lattice Theory: First Concepts and Distributive Lattices. San Francisco, CA: W. H. Freeman, pp. 35-36, 1971.




© 1996-9 Eric W. Weisstein
1999-05-24