Corollary 1

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

Commutative Algebra, chapter VI, § 1. Valuation rings

*Every valuation ring of the field $\mathbf{Q}$ and distinct from $\mathbf{Q}$ is of the form $\mathbf{Z}_{(p)}$ where $p$ is a prime number.

Every subring of $\mathbf{Q}$ contains $\mathbf{Z}$ .

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

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