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Version 7 |
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A \PMlinkname{lattice}{Lattice} is said to be \emph{distributive} if it satisifes either (and therefore both) of the \PMlinkname{distributive laws}{Distributive}:
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A lattice is said to be \emph{\PMlinkescapetext{distributive}} if it satisifes either (and therefore both) of the distributive laws:
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| \begin{itemize} |
\begin{itemize} |
| \item $x \land (y \lor z) = (x \land y) \lor (x \land z)$ |
\item $x \land (y \lor z) = (x \land y) \lor (x \land z)$ |
| \item $x \lor (y \land z) = (x \lor y) \land (x \lor z)$ |
\item $x \lor (y \land z) = (x \lor y) \land (x \lor z)$ |
| \end{itemize} |
\end{itemize} |
| Every distributive lattice is \PMlinkname{modular}{ModularLattice}. |
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