additive form of Hilbert’s theorem 90

Let $L/K$ be a finite cyclic Galois extension and $\sigma$ a generator of $\mathrm{Gal}(L/K)$. An element $y\in L$ satisfies $\mathrm{Tr}(y)=0$ if and only if there exists $x\in L$ satisfying $y=x-\sigma (x)$. Here $\mathrm{Tr}$ 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