stronger Hilbert theorem 90

Let K be a field and let K¯ be an algebraic closureMathworldPlanetmath of K. By K¯+ we denote the abelian groupMathworldPlanetmath (K¯,+) and similarly K¯=(K¯,) (here the operation is multiplication). Also we let


be the absolute Galois group of K.

Theorem 1 (Hilbert 90).

Let K be a field.

  1. 1.
  2. 2.
  3. 3.

    If char(K), the characteristicPlanetmathPlanetmath of K, does not divide m (or char(K)=0) then


    where μm denotes the set of all mth-roots of unityMathworldPlanetmath.


Title stronger Hilbert theorem 90
Canonical name StrongerHilbertTheorem90
Date of creation 2013-03-22 13:50:27
Last modified on 2013-03-22 13:50:27
Owner alozano (2414)
Last modified by alozano (2414)
Numerical id 6
Author alozano (2414)
Entry type Theorem
Classification msc 20J06
Synonym Hilbert 90
Related topic HilbertTheorem90