Remark 1

Tag 0CO6, permanent. Cite it as [Bourbaki, Tag 0CO6].

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

The integer $c_M$ is positive by lemma 2. One may have $M \neq 0$ and $c_M = 0$ (cf. prop. 2).

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

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