Axiom:Huntington Algebra Axioms

From ProofWiki
Jump to navigation Jump to search

Definition

An algebraic structure $\struct {S, \circ, *}$ is a Huntington algebra if and only if $\struct {S, \circ, *}$ satisfies the 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 $e^\circ \ne e^*$      
\((\text {HA} 4)\)   $:$   $\forall a \in S: \exists a' \in S: a \circ a' = e^*, a * a' = e^\circ$      


These criteria are called the Huntington algebra axioms.

Also see


Source of Name

This entry was named for Edward Vermilye Huntington.