Corollary 1

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

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

With the same hypotheses and notation, suppose further that v is discrete and L separable. Then

\sum_{i=1}^{s} e(v_i'/v) f(v_i'/v) = n.

The integral closure B of A is then a free A-module of rank $n$ , since A is a principal ideal domain (Chapter V, § 1, no. 6, Corollary 2 to Proposition 18).

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

Cited by

Nothing.

Cites

Chapter V, § 1, no. 6, Corollary 2 to Proposition 18