# Artin-Schreier theorem

From Encyclopedia of Mathematics

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