Simple extension of a simple extension

Asked Feb 15 '22 at 08:12

Active Feb 15 '22 at 08:12

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Let $E / F$ be a field extension, and let $\alpha, \beta \in E$. Is it true in general that $\left(F(\alpha)\right)(\beta) = F(\alpha, \beta)$? (I.e., that $F'(\beta) = F(\alpha, \beta)$ where $F' = F(\alpha)$.)

I haven't been able to find a counterexample.

asked Feb 15 '22 at 08:12

Anakhand

2,572

yes it's always true. – Surb Feb 15 '22 at 08:17
I would even say it is more or less the definition. – Captain Lama Feb 15 '22 at 08:19

Simple extension of a simple extension

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