Corollary

Tag 0D7S, permanent. Cite it as [Bourbaki, Tag 0D7S].

Let $A$ be a $k$ -algebra essentially of finite type and $B$ a noetherian $k$ -algebra. Then the ring $A \otimes_k B$ is noetherian.

In fact, it is a $B$ -algebra essentially of finite type (prop. 2, d)), and one applies Proposition 1.

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

Cited by

Nothing.

Nothing.