Lemma 1

Tag 04W6, permanent. Cite it as [Bourbaki, Tag 04W6].

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

Let $\mathbf{K}, \mathbf{K}', \mathbf{K}''$ be three fields such that $K \subset K' \subset K''$ , $v''$ a valuation on $K''$ and $v$ and $v'$ its restriction to $\mathbf{K}$ and $\mathbf{K}'$ . Then there are the relations:

(1)\quad e(v''/v) = e(v''/v') e(v'/v), \qquad f(v''/v) = f(v''/v') f(v'/v).

This is obvious.

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

Cited by

Theorem 1, § 8
Theorem 2, § 8
Corollary 4, § 8
Lemma 5, § 4

Cites

Nothing.