Bourbaki

Corollary 1

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

Commutative Algebra, chapter VI, § 8. Extensions of a valuation to an algebraic extension

If K is complete with respect to v and v is not improper, two valuations on L extending v are dependent.

This follows since K^⊗KL=L\hat{K} \otimes_K L = L.

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

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Cites

Nothing.

Transcribed from the printed volume. Not translated.