Corollary 1

Tag 0467, permanent. Cite it as [Bourbaki, Tag 0467].

Commutative Algebra, chapter II, § 2. Rings and modules of fractions

Let $N_1, N_2$ be two submodules of an $A$ -module $M$ . For $S^{-1}N_1 \subset S^{-1}N_2$ , it is necessary and sufficient that the saturation of $N_1$ with respect to $S$ be contained in that of $N_2$ .

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

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