Remark 2

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

Commutative Algebra, chapter VIII, § 4. Séries de Hilbert-Samuel

Suppose q contained in the radical of A; then $\dim(\hat{M}) = \dim(M)$ (loc. cit., cor. 1), hence $d(M) = \dim(M)$ .

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

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