Corollary

Tag 0D90, permanent. Cite it as [Bourbaki, Tag 0D90].

Commutative Algebra, chapter X, § 7. Algèbres lisses

Let $k$ be a field, $K$ a separable extension of $k$ and $A$ a linearly topologized $K$ -algebra. If $A$ is formally smooth over $K$ , it is formally smooth over $k$ .

This follows from the theorem and prop. 3 a) of No. 2.

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

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