Definition 5
Tag 06KX, permanent. Cite it as [Bourbaki, Tag 06KX].
Algebra, chapter V, § 7. Separable algebraic extensions
— Let K be a field. By a separable algebraic closure, or (by abuse of language) separable closure of K we understand any extension E of K which is algebraic and separable over K, and such that the field E is separably closed.
When K is perfect, there is complete identity between the notions of separable closure and algebraic closure of K (V, p. 36, Prop. 2 and p. 43, Cor. 1).
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.
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