Remark

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

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

Proposition 2 (b) shows that every composite extension of $\hat{K}$ and L over K (Algebra, Chapter VIII, § 8) is isomorphic to one of the completions $\hat{L}_i$ and that these are composite extensions no two of which are isomorphic.

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

Cited by

Nothing.

Cites

Proposition 2
*Algebra*, Chapter VIII, § 8