Axiom:Huntington Algebra Axioms
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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.