Bourbaki

Remark

Tag 0D10, permanent. Cite it as [Bourbaki, Tag 0D10].

Commutative Algebra, chapter X, § 1. Profondeur

Recall that, under the preceding assumptions,

dim⁡B(M⊗AN)=dim⁡A(M)+dim⁡B(κA⊗AN) \dim_B(M \otimes_A N) = \dim_A(M) + \dim_B(\kappa_A \otimes_A N)
(VIII, § 3, No. 4, Prop. 7).

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

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