Proposition 5

Tag 06M0, permanent. Cite it as [Bourbaki, Tag 06M0].

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

— Let E be an extension of K contained in $\Omega$ and N the quasi-Galois extension generated by E. If A is a subset of $\Omega$ such that $E = K(A)$ then $N = K(B)$ , where B is the set of elements of $\Omega$ which are conjugate to an element of A.

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

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