Bourbaki

Corollary 2

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

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

Let h and h' be the heights of v and v'. Then

s(v′/v)+h′≤d(K′/K)+h. s(v'/v) + h' \leq d(K'/K) + h.
By Proposition 3, h′≤r(v′/v)+hh' \leq r(v'/v) + h.

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

Cited by

Nothing.

Cites

Transcribed from the printed volume. Not translated.