additive form of Hilbert’s theorem 90

Let L/K be a finite cyclic Galois extensionMathworldPlanetmath and σ a generatorPlanetmathPlanetmathPlanetmath of Gal(L/K). An element yL satisfies Tr(y)=0 if and only if there exists xL satisfying y=x-σ(x). Here Tr denotes the trace in L/K.

Title additive form of Hilbert’s theorem 90
Canonical name AdditiveFormOfHilbertsTheorem90
Date of creation 2013-03-22 15:20:35
Last modified on 2013-03-22 15:20:35
Owner mathwizard (128)
Last modified by mathwizard (128)
Numerical id 7
Author mathwizard (128)
Entry type Theorem
Classification msc 11R32
Classification msc 12F10
Related topic HilbertTheorem90