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).
|[a1]||S. Lang, "Algebra" , Addison-Wesley (1974)|
Artin-Schreier theorem. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Artin-Schreier_theorem&oldid=17088