Hurwitz's Theorem (Normed Division Algebras)

Theorem

The only normed division algebras over the real numbers are:

the real numbers $\R$ themselves

the complex numbers $\C$

the quaternions $\H$

the octonions $\mathbb O$

Proof

This theorem requires a proof. You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by crafting such a proof. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{ProofWanted}} from the code. If you would welcome a second opinion as to whether your work is correct, add a call to {{Proofread}} the page.

Source of Name

This entry was named for Adolf Hurwitz.

Sources

• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Cayley algebra (J.T. Graves, 1843)