Remark 4

Tag 0D1S, permanent. Cite it as [Bourbaki, Tag 0D1S].

Commutative Algebra, chapter X, § 1. Profondeur

$\mathrm{ht}(p) \geq 2$ . Since $A_p$ is of depth $\geq 2$ (Cor. of Prop. 16), the same is true of $B_q$ by loc. cit.

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

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