Proposition 12

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

Algebra, chapter V, § 10. Galois extensions

— For every finite $\Gamma$ -set $X$ the algebra $\Theta(X)$ is etale over $K$ , of degree equal to the cardinal of $X$ . Moreover, every etale algebra over $K$ is isomorphic to an algebra of the form $\Theta(X)$ .

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

Cited by

Remark 6, § 16

Cites

Nothing.