The only nonassociative division algebra with real scalars. There is an 8-square identity corresponding to this algebra.
The elements of a Cayley algebra are called Cayley numbers or octonions, and the multiplication table for any Cayley algebra over a field with field characteristic may be taken as shown in the following table, where , , ..., are a bases over and , , and are nonzero elements of (Schafer 1996, pp. 5-6).