Remark

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

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

Conversely, let $f$ be a place of K with values in $K'$ and $f'$ a place of $K'$ with values in $K''$ . Then $f' \circ f$ is a place of K whose ring is contained in the ring of the place $f$ .

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

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