Corollary

Tag 044A, permanent. Cite it as [Bourbaki, Tag 044A].

Commutative Algebra, chapter I, § 3. Faithfully flat modules

Let $C$ be a commutative ring and $E$ and $F$ two faithfully flat $C$ -modules. Then the $C$ -module $E \otimes_C F$ is faithfully flat.

Apply Proposition 4 with $R = S = C$ .

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

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