Definition 4

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

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

Let G be a totally ordered commutative group and H a subgroup of G of finite index. The number of major subsets of G consisting of strictly positive elements and containing all the elements > O of H is called the initial index of H in G and denoted by $\varepsilon(G, H)$ .

This initial index is a natural number by virtue of the following proposition:

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

Cited by

Proposition 3, § 8

Cites

Nothing.