Corollary 1

Tag 0430, permanent. Cite it as [Bourbaki, Tag 0430].

Commutative Algebra, chapter I, § 2. Flat modules

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

$F$ is a $(C, C)$ -bimodule and it is sufficient to apply Proposition 8 with $B = A = C$ .

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

Cited by