Every finite separable field extension is generated by one element.Suggest a slogan
Let \(L/k\) be a finite separable field extension. Then \(L/k\) is simple: there exists \(\alpha\in L\) with \(L=k(\alpha)\).
Primitive element theorem
T-3HPWT
T-3HPWT
Let \(L/k\) be a finite separable field extension. Then \(L/k\) is simple: there exists \(\alpha\in L\) with \(L=k(\alpha)\).