Nonassociative Division Algebra with Real Scalars has Dimension of Power of 2

From ProofWiki
Jump to navigation Jump to search

Theorem

Let $A$ be a nonassociative division algebra with real scalars.


Then the dimension of $A$ is a power of $2$.


Proof


Historical Note

Nonassociative Division Algebra with Real Scalars has Dimension of Power of 2 was demonstrated by Heinz Hopf in $1940$.


Sources