Corollary 1

Tag 06UP, permanent. Cite it as [Bourbaki, Tag 06UP].

Algebra, chapter V, § 16. Differential criteria of separability

— We have $\Omega_K(L) = 0$ if $L$ is algebraic and separable over $K$ .

The corollary follows from Prop. 4, a) because the vector $L$ -space $\Omega_K(L)$ is generated by the image of the canonical $K$ -derivation $d_{L/K} : L \to \Omega_K(L)$ .

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

Cited by

Remark, § 16
Corollary 2, § 16

Cites

Prop. 4