Proposition 6

Tag 04T9, permanent. Cite it as [Bourbaki, Tag 04T9].

Commutative Algebra, chapter VI, § 3. Valuations

Let $K$ be a field, $A$ a subring of $K$ and $x$ an element of $K$ . For $x$ to be integral over $A$ , it is necessary and sufficient that every valuation on $K$ which is positive on $A$ be positive at $x$ .

From now on, we shall in general leave to the reader the trouble of performing translations analogous to the above.

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

Cited by

Proposition 6, § 8

Cites

Nothing.