# Artin–Zorn theorem

In mathematics, the **Artin–Zorn theorem**, named after Emil Artin and Max Zorn, states that any finite alternative division ring is necessarily a finite field. It was first published in 1930 by Zorn, but in his publication Zorn credited it to Artin.[1][2]

The Artin–Zorn theorem is a generalization of the Wedderburn theorem, which states that finite associative division rings are fields. As a geometric consequence, every finite Moufang plane is the classical projective plane over a finite field.[3][4]

## References

- Zorn, M. (1930), "Theorie der alternativen Ringe",
*Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg*,**8**: 123–147. - Lüneburg, Heinz (2001), "On the early history of Galois fields", in Jungnickel, Dieter; Niederreiter, Harald (eds.),
*Finite fields and applications: proceedings of the Fifth International Conference on Finite Fields and Applications Fq5, held at the University of Augsburg, Germany, August 2–6, 1999*, Springer-Verlag, pp. 341–355, ISBN 978-3-540-41109-3, MR 1849100. - Shult, Ernest (2011),
*Points and Lines: Characterizing the Classical Geometries*, Universitext, Springer-Verlag, p. 123, ISBN 978-3-642-15626-7. - McCrimmon, Kevin (2004),
*A taste of Jordan algebras*, Universitext, Springer-Verlag, p. 34, ISBN 978-0-387-95447-9.

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