Corollary

Tag 04KX, permanent. Cite it as [Bourbaki, Tag 04KX].

Commutative Algebra, chapter IV, § 2. Primary decomposition

The mappings

D_I(M/N) \to D_J(M/N') \quad \text{and} \quad D_I(M/N) \to D_J(S^{-1}M/S^{-1}N)

defined in Proposition 6 (i) are surjective.

Proposition 6 (iii) shows that the mapping $D_I(M/N) \to D_J(M/N')$ is surjective and Proposition 6 (ii) then shows that the mapping

D_I(M/N) \to D_J(S^{-1}M/S^{-1}N)

is surjective.

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

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