Bourbaki

Proposition 2

Tag 06LD, permanent. Cite it as [Bourbaki, Tag 06LD].

Algebra, chapter V, § 8. Norms and traces

— Let F be an extension of finite degree of K and E a subextension of F. Then for every x∈Fx \in F we have

TrF/K(x)=TrE/K(TrF/E(x))NF/K(x)=NE/K(NF/E(x)). \text{Tr}_{F/K}(x) = \text{Tr}_{E/K}(\text{Tr}_{F/E}(x)) \\ \text{N}_{F/K}(x) = \text{N}_{E/K}(\text{N}_{F/E}(x)) .

Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.

Cited by

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Cites

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Transcribed from the printed edition, 2003, Springer. Not translated.