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Situation 9.12.7. Here $F$ be a field and $K/F$ is a finite extension generated by elements $\alpha _1, \ldots , \alpha _ n \in K$. We set $K_0 = F$ and

\[ K_ i = F(\alpha _1, \ldots , \alpha _ i) \]

to obtain a tower of finite extensions $K = K_ n / K_{n - 1} / \ldots / K_0 = F$. Denote $P_ i$ the minimal polynomial of $\alpha _ i$ over $K_{i - 1}$. Finally, we fix an algebraic closure $\overline{F}$ of $F$.

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