Proposition 7

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

Commutative Algebra, chapter VI, § 4. The height of a valuation

For a valuation on a field to be of height 1, it is necessary and sufficient that its order group be isomorphic to a non-zero ordered subgroup of \mathbf{R}.

This follows in fact from the following proposition:

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

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Cites

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