Bruck-Kleinfeld theorem on alternative division rings

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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:

  1. It is associative, and hence a division ring in the usual sense of the term.
  2. It is an octonion algebra arising from a Cayley-Dickson construction.

Related facts

Applications