Example

Tag 06S0, permanent. Cite it as [Bourbaki, Tag 06S0].

Algebra, chapter V, § 14. Transcendental extensions

— A pure basis is a transcendence basis. On the other hand, if E is a pure extension of K, a transcendence basis of E over K is not always a pure basis of E. For example, in $K(X)$ , $\{X^2\}$ is a transcendence basis but does not generate $K(X)$ .

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

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