# 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 |
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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 |