Corollary 3

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

Commutative Algebra, chapter V, § 2. The lift of prime ideals

With the hypotheses and notation of Corollary 2, if $A$ is semi-local, so is $A'$ .

For every maximal ideal $m'$ of $A'$ , $m' \cap A$ is a maximal ideal of $A$ (no. 1, Proposition 1); the corollary then follows from Corollary 2, since by hypothesis the set of maximal ideals of $A$ is finite.

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

Cited by

Nothing.

Cites

no. 1, Proposition 1
Corollary 2