Definition:Huntington Algebra

Definition
A Huntington algebra is an algebraic structure $\left({S, \circ, *}\right)$ such that:

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

A Huntington algebra can also be considered as a mathematical system $\left\{{S, O, A}\right\}$ where $O = \left\{{\circ, *}\right\}$ and $A$ consists of the set of axioms $(HA \ 0)$ to $(HA \ 4)$ 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 $\left({S, \circ}\right)$ nor $\left({S, *}\right)$ 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

 * Boolean Ring
 * Boolean Algebra

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