Bourbaki

Definition 2

Tag 0D9R, permanent. Cite it as [Bourbaki, Tag 0D9R].

Commutative Algebra, chapter X, § 7. Algèbres lisses

Let AA be a noetherian ring. An AA-algebra BB is said to be smooth if it is essentially of finite type and if it satisfies the equivalent conditions of theorem 4.

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

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