Remark
Tag 06KV, permanent. Cite it as [Bourbaki, Tag 06KV].
Algebra, V, p. 45, § 7. Separable algebraic extensions
Let E be an algebraic extension of K and E, the relative p-radical closure of E in K (V, p. 25). Then E, is the largest subextension of E which is p-radical over K (V, p. 25, Prop. 2). However, E is in general not separable over E, (V, p. 152, Ex. 2); for the case of quasi-Galois extensions see V, p. 76.
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.
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