\(\omega_ 0\)-generated field extensions (Q1071814)

Let \(L\supset K\) be fields of characteristic \(p\neq 0\). L is \(\omega_ 0\)-generated over K if L is infinite-dimensional over K and yet every proper intermediate field is finite dimensional over K. This paper presents an example \(L\supset K\) of an \(\omega_ 0\)-generated purely inseparable field extension where \([K^{p^{-n}}\cap L: K]=p^{2n}\) for all n.