# Definition:Brouwerian Lattice

## 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.