# Category:Huntington Algebras

A Huntington algebra is an algebraic structure $\struct {S, \circ, *}$ such that:
 $(\text {HA} 0)$ $:$ $S$ is closed under both $\circ$ and $*$ $(\text {HA} 1)$ $:$ Both $\circ$ and $*$ are commutative $(\text {HA} 2)$ $:$ Both $\circ$ and $*$ distribute over the other $(\text {HA} 3)$ $:$ Both $\circ$ and $*$ have identities $e^\circ$ and $e^*$ respectively, where $e^\circ \ne e^*$ $(\text {HA} 4)$ $:$ $\forall a \in S: \exists a' \in S: a \circ a' = e^*, a * a' = e^\circ$
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.