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

## Theorem

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

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

## Historical Note

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