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.