Definition 1

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

Commutative Algebra, chapter VI, § 1. Valuation rings

Let $A$ and $B$ be two local rings. $B$ is said to dominate $A$ if $A$ is a subring of $B$ and $m(A) = A \cap m(B)$ .

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

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