Corollary 1

Tag 04Q5, permanent. Cite it as [Bourbaki, Tag 04Q5].

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

Under the hypotheses Of Theorem 2 the rings $A/p$ and $A^\mathbf{Z}/(p' \cap A^\mathbf{Z})$ have the same field Of fractions and the maximal ideal of the local ring $(A^\mathbf{Z})'_{p' \cap A^\mathbf{Z}}$ is generated by $p$ .

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

Cited by

Nothing.

Cites

Theorem 2