Corollary 3

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

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

— *For an element x of L to be algebraic over K it is necessary and sufficient that $dx = 0$ in $\Omega_K(L)$ . In particular, for L to be an algebraic extension of K it is necessary and sufficient that $\Omega_K(L) = 0$ . This follows immediately from Cor. 2 on taking $E = K$ .

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

Cited by

Nothing.

Cites

Cor. 2