Definition:Huntington Algebra

Definition
A Huntington algebra is an algebraic structure $\struct {S, \circ, *}$ such that:

The element $a'$ in $(\text {HA} 4)$ is often called the complement of $a$.

A Huntington algebra can also be considered as a mathematical system $\set {S, O, A}$ where $O = \set {\circ, *}$ and $A$ consists of the set of axioms $(\text {HA} 0)$ to $(\text {HA}  4)$ as defined above.

At first glance, a Huntington algebra looks like a ring, except with the double distributivity thing in it.

But note that, despite the fact that Operations of Huntington Algebra are Associative, neither $\struct {S, \circ}$ nor $\struct {S, *}$ are actually groups.

Also known as
This mathematical structure is called variously such names as: However, modern usage tends to give these terms different meanings.
 * Boolean ring
 * Boolean algebra

Also see

 * Definition:Boolean Ring
 * Definition:Boolean Algebra

Category:Definitions/Abstract Algebra Category:Definitions/Boolean Algebras