Remark

Tag 04Y8, permanent. Cite it as [Bourbaki, Tag 04Y8].

Commutative Algebra, chapter VI, § 10. Extensions of a valuation to a transcendental extension

It should not be thought that the two types of extensions of v to K(X) which we have just met are the only ones; there may exist a third type of extension, where $\Gamma'/\Gamma$ is a torsion group and $k'$ a (not necessarily finite) algebraic extension of $k$ . This third type is not necessarily provided by the procedure described in Lemma 1 (cf. § 3, Exercise 1).

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

Cited by

Nothing.

Cites

Lemma 1
§ 3, Exercise 1