Proposition 1

Tag 0609, permanent. Cite it as [Bourbaki, Tag 0609].

Let $E, F$ be two $A$ -algebras and $a$ (resp. $b$ ) a two-sided ideal of $E$ (resp. $F$ ). Then the canonical $A$ -module isomorphism

(E/a) \otimes (E/b) \to (E \otimes F)/(\operatorname{Im}(a \otimes F) + \operatorname{Im}(E \otimes b))

(II, § 3, no. 6, Corollary 1 to Proposition 6) is an algebra isomorphism.

This follows from (1) and the definition given loc. cit.

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

Cited by

Nothing.