Corollary 2

Tag 0D0Q, permanent. Cite it as [Bourbaki, Tag 0D0Q].

Commutative Algebra, chapter X, § 1. Profondeur

Let $A$ be a noetherian local ring, $M$ a nonzero finitely generated $A$ -module. One has

\operatorname{prof}_A(M) \leqslant \dim_A(M) < +\infty .

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

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