# Definition:Brouwerian Lattice

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## Definition

Let $\left({L, \wedge, \vee, \preceq}\right)$ be a lattice.

Then $\left({L, \wedge, \vee, \preceq}\right)$ is a **Brouwerian lattice** if and only if:

- for each $x, y \in L$: $x$ has a relative pseudocomplement with respect to $y$.

This pseudocomplement is denoted $x \to y$.

## Also known as

A **Brouwerian lattice** is also known as a **relatively pseudocomplemented lattice** .

## Source of Name

This entry was named for Luitzen Egbertus Jan Brouwer.

## Sources

*This article incorporates material from Brouwerian lattice on PlanetMath, which is licensed under the Creative Commons Attribution/Share-Alike License.*