Category:Huntington Algebras

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This category contains results about Huntington Algebras.

An algebraic structure $\struct {S, \circ, *}$ is a Huntington algebra if and only if $\struct {S, \circ, *}$ satisfies the Huntington algebra axioms:

\((\text {HA} 0)\)   $:$   $S$ 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.

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