\begin{definition}[Definition:Radical Extension]
Let $L / F$ be a field extension.
Then $L$ is a '''radical extension of $F$''' {{iff}} there exist $\alpha_1, \ldots, \alpha_m \in F$ and $n_1, \ldots, n_2 \in \Z_{>0}$ such that:
:$(1): \quad L = K \sqbrk {\alpha_1, \ldots, \alpha_m}$
:$(2): \quad \alpha_1^{n_1} \in F$
:$(3): \quad \forall i \in \N_m: \alpha_i^{n_i} \in F \sqbrk {\alpha_1, \ldots, \alpha_{i-1} }$
where $K \sqbrk {\alpha_1, \ldots, \alpha_m}$ and $F \sqbrk {\alpha_1, \ldots, \alpha_{i-1} }$ are generated field extensions.
Category:Definitions/Field Extensions
\end{definition}