# Artin-Schreier theorem

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The Artin–Schreier theorem for extensions of degree of a field of characteristic states that every such Galois extension is of the form , where is the root of a polynomial of the form , an Artin–Schreier polynomial.

If is a function field, these polynomials define Artin–Schreier curves, which in turn give rise to Artin–Schreier codes (cf. Artin–Schreier code).

#### References

 [a1] S. Lang, "Algebra" , Addison-Wesley (1974)
How to Cite This Entry:
Artin-Schreier theorem. Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Artin-Schreier_theorem&oldid=17088
This article was adapted from an original article by M. Hazewinkel (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article