Corollary 1

Tag 060A, permanent. Cite it as [Bourbaki, Tag 060A].

Algebra, chapter III, § 4. Tensor products of algebras

Let $E$ be an $A$ -algebra and $a$ an ideal of $A$ . Then the $A$ -module $aE$ is a two-sided ideal of $E$ and the canonical $(A/a)$ -module isomorphism

(A/a) \otimes_A E \to E/aE

is an $(A/a)$ *-algebra isomorphism*.

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

Cited by

§ 10. Derivations

Cites

Nothing.