A theorem of Wedderburn says that finite division ring is field.

Here, ring means "ring with unity and is also associative".

In particular, finite division (associative) algebras are fields.

I was trying to get examples of following kind of algebras.

Q 1. What are the examples of finite division non-associative algebras over a field of order $p$, a prime?

Q.2 Where can I find the properties of algebras in Q. 1?

Note that there are simple examples of finite non-associative algebras, namely Lie algebras over a finite field of finite dimension; but they are not necessarily (perhaps never) division algebras.

  • $\begingroup$ Relevant: math.stackexchange.com/questions/614634/… $\endgroup$ – pregunton Sep 17 '17 at 10:47
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    $\begingroup$ Have you looked at Glynn's On finite division algebras? $\endgroup$ – Kimball Sep 17 '17 at 23:42
  • $\begingroup$ @pregunton: the link you stated contains associative division rings, whereas my question is about non-associative only. $\endgroup$ – Beginner Sep 20 '17 at 6:56

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