Corollary

Tag 06J6, permanent. Cite it as [Bourbaki, Tag 06J6].

Algebra, V, p. 25, § 5. p-radical extensions

— For an extension E of a field K to be a perfect closure of K it is necessary and sufficient that it should be a p-radical extension of K and that the field E should be perfect.

The Corollary is trivial when $p = 1$ ; suppose then that $p \neq 1$ . The stated conditions are necessary by V, p. 5, Th. 3 ; they are sufficient by Prop. 3.

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

Cited by

Nothing.

Cites

Prop. 3