noun
Usage: usually capitalized B
: a set that is closed under two commutative binary operations and that can be described by any of various systems of postulates all of which can be deduced from the postulates that an identity element exists for each operation, that each operation is distributive over the other, and that for every element in the set there is another element which when combined with the first under one of the operations yields the identity element of the other operation
under the operations of taking intersections and unions, the subsets of a given set form a Boolean algebra