nLab
atomic Boolean algebra

Atomic Boolean algebras

Definition

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

A Boolean algebra AA is atomic if we have b= Ia ib = \bigvee_I a_i for every bAb \in A, where {a i} I\{a_i\}_I is some set of atoms in AA.

Properties

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