The Name for $\mathbb{R}$, $\mathbb{C}$, $\mathbb{H}$ and $\mathbb{O}$ Exclusively Algebras? The Wikipedia page for Normed Division Algebras has been redirected to Normed Algebras and the explanation given is that $\mathbb{R}$, $\mathbb{C}$, $\mathbb{H}$ and $\mathbb{O}$ algebras are not the only normed division algebras.  

What is the name for the class of algebras consisting of $\mathbb{R}$, $\mathbb{C}$, $\mathbb{H}$ and $\mathbb{O}$ exclusively?
Euclidean Hurwitz algebras

"Theorem. The only Euclidean Hurwitz algebras are the real numbers, the complex numbers, the quaternions and the octonions."
This list of algebras stems from the Frobenius theorem for finite division algebras over the real numbers. As one goes further down the list, properties of the real numbers are lost along the way.


Real numbers: totally ordered, commutative, associative
Complex numbers: commutative, associative
Quaternions: associative
Octonions: none of the above