Definition:Radical Extension

Definition
Suppose $L/F$ is a field extension.

We say that $L$ is a radical extension of $F$ provided that there are $\alpha_{1},\ldots,\alpha_{m} \in F$ and $n_{1},\ldots,n_{2} \in \mathbb{Z}_{>0}$ such that


 * $\bullet \: L=K[\alpha_{1},\ldots,\alpha_{m}]$


 * $\bullet \: \alpha_{1}^{n_{1}} \in F$


 * $\bullet \: \forall i \in \mathbb{N}_{m}, \alpha_{i}^{n_{i}} \in F[\alpha_{1},\ldots,\alpha_{i-1}]$