Definition 3

Tag 04U8, permanent. Cite it as [Bourbaki, Tag 04U8].

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

The height of the order group of a valuation is called the height of that valuation.

For example a discrete valuation is of height 1. Only improper valuations are of height 0. Propositions 1 and 4 imply:

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

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