Corollary 2

Tag 06M2, permanent. Cite it as [Bourbaki, Tag 06M2].

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

— Every quasi-Galois extension N of K is the union of quasi-Galois subextensions of N of finite degree over K. Let $x \in N$ and let $N_x$ be the quasi-Galois extension of K generated by $\{x\}$ . Since $K(x)$ is of finite degree over K, the same is true of $N_x$ (Cor. 1) and we have $x \in N_x$ .

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

Cited by

Nothing.

Cites

Cor. 1