Bruck-Kleinfeld theorem on alternative division rings
(Redirected from Bruck-Kleinfeld theorem)
Name
The result is due to Bruck and Kleinfeld and is termed the Bruck-Kleinfeld theorem.
Statement
There are only two possibilities for an alternative division ring. It can be either of these:
- It is associative, and hence a division ring in the usual sense of the term.
- It is an octonion algebra arising from a Cayley-Dickson construction.