Corollary 1

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

Algebra, chapter V, § 9. Conjugate elements and quasi-Galois extensions

— For an extension E of K contained in $\Omega$ to be quasi-Galois it is necessary and sufficient that it should be identical to all its conjugates over K.

This follows from Prop. 1, a) (V, p. 52) and the equivalence of the conditions a) and c) of Prop. 3.

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

Cited by

Theorem 1, § 10
Proposition 3, § 9
Proposition 4, § 9

Cites

Prop. 1, a) (V, p. 52
Prop. 3