Corollary 1

Tag 0D09, permanent. Cite it as [Bourbaki, Tag 0D09].

Commutative Algebra, chapter X, § 1. Profondeur

Let m be an integer > 0 and let J' be an ideal of A which contains J^m. One has prof_A(J ; M) \leq prof_A(J' ; M).

In fact J^m annihilates the A-module A/J', hence Ext^i_A(A/J', M) is zero for every integer i < prof_A(J ; M) (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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