Remark 2

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

Algebra, V, p. 112, § 14. Transcendental extensions

It may happen that E is algebraically disjoint from F over K, but not over a subfield $K_{\|}$ of K. \* For example C is algebraically disjoint from itself over R but not over $\mathbf{Q}$ . \*

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

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