In abstract algebra

Abstract algebra

Abstract algebra is the subject area of mathematics that studies algebraic structures, such as groups, rings, fields, modules, vector spaces, and algebras...

, a Boolean algebra or Boolean lattice is a complemented

Complemented lattice

In the mathematical discipline of order theory, a complemented lattice is a bounded lattice in which every element a has a complement, i.e. an element b satisfying a ∨ b = 1 and a ∧ b = 0....

 distributive

Distributive lattice

In mathematics, distributive lattices are lattices for which the operations of join and meet distribute over each other. The prototypical examples of such structures are collections of sets for which the lattice operations can be given by set union and intersection...

 lattice

Lattice (order)

In mathematics, a lattice is a partially ordered set in which any two elements have a unique supremum and an infimum . Lattices can also be characterized as algebraic structures satisfying certain axiomatic identities...

. This type of algebraic structure

Algebraic structure

In abstract algebra, an algebraic structure consists of one or more sets, called underlying sets or carriers or sorts, closed under one or more operations, satisfying some axioms. Abstract algebra is primarily the study of algebraic structures and their properties...

 captures essential properties of both set operations and logic

Logic

In philosophy, Logic is the formal systematic study of the principles of valid inference and correct reasoning. Logic is used in most intellectual activities, but is studied primarily in the disciplines of philosophy, mathematics, semantics, and computer science...

 operations. A Boolean algebra can be seen as a generalization of a power set algebra or a field of sets. It is also a special case of De Morgan algebra

De Morgan algebra

In mathematics, a De Morgan algebra is a structure A =  such that:* is a bounded distributive lattice, and...

 and Kleene algebra

Kleene algebra

In mathematics, a Kleene algebra is either of two different things:* A bounded distributive lattice with an involution satisfying De Morgan's laws , additionally satisfying the inequality x∧−x ≤ y∨−y. Kleene algebras are subclasses of Ockham algebras...

.



The term "Boolean algebra" honors George Boole

George Boole

George Boole was an English mathematician and philosopher.As the inventor of Boolean logic—the basis of modern digital computer logic—Boole is regarded in hindsight as a founder of the field of computer science. Boole said,...

 (1815–1864), a self-educated English mathematician.