Let \(F\) be a field, \(K\subseteq F\) a subfield, and \(\alpha\in F\). The subfield generated by \(K\) and \(\alpha\), written \(K(\alpha)\), is the smallest subfield of \(F\) containing \(K\) and \(\alpha\), that is, the intersection of all subfields of \(F\) that contain \(K\cup\theset{\alpha}\).
For $\alpha$ in an extension $F \supset K$, what is $K(\alpha)$?
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FD-QPNDASubfield $K(\alpha)$ generated by an element of an extension fieldvariant-of