Corollary 2
Tag 04WZ, permanent. Cite it as [Bourbaki, Tag 04WZ].
Commutative Algebra, chapter VI, § 8. Extensions of a valuation to an algebraic extension
Let K be a field, f a place of K (resp. v a valuation on K) and L a radicial extension of K. Then all the extensions of f (resp. v) to L are equivalent.
L is a quasi-Galois extension and its only automorphism is the identity. Corollary 2 therefore follows from Proposition 7 (resp. Corollary 1).
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.
Cited by
Nothing.