# Atomic Boolean algebras

## Definition

Given an element $a$ of a Boolean algebra (or other poset) $A$, recall that $a$ is atomic in $A$ if $a$ is minimal among non-trivial (non-bottom) elements of $A$. That is, given any $b \in A$ such that $b \leq a$, either $b = 0$ or $b = a$.

A Boolean algebra $A$ is atomic if we have $b = \bigvee_I a_i$ for every $b \in A$, where $\{a_i\}_I$ is some set of atoms in $A$.

## Properties

Revised on March 7, 2012 02:13:32 by Toby Bartels (98.23.141.35)