\begin{definition}[Definition:Huntington Algebra]
A '''Huntington algebra''' is an algebraic structure $\struct {S, \circ, *}$ such that:
{{begin-axiom}}
{{axiom | n = \text {HA} 0
        | lc=
        | t = $S$ is closed under both $\circ$ and $*$
}}
{{axiom | n = \text {HA} 1
        | lc=
        | t = Both $\circ$ and $*$ are commutative
}}
{{axiom | n = \text {HA} 2
        | lc=
        | t = Both $\circ$ and $*$ distribute over the other
}}
{{axiom | n = \text {HA} 3
        | lc=
        | t = Both $\circ$ and $*$ have identities $e^\circ$ and $e^*$ respectively, where $e^\circ \ne e^*$
}}
{{axiom | n = \text {HA} 4
        | lc=
        | t = $\forall a \in S: \exists a' \in S: a \circ a' = e^*, a * a' = e^\circ$
}}
{{end-axiom}}
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.
<pre>{{expand|example?}}
{{expand|compare to Boolean algebra. Also, it would be nice to make the exposition and perhaps even the notation parallel, if these structures are as similar as they appear, unless conventional notation is firmly fixed.}}</pre>
\end{definition}