Radical extension

This article defines a field property: a property that can be evaluated to true/false for any field.
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Definition

For finite extensions

Suppose $L$ is a finite extension of a field $K$. We say that $L$ is a radical extension if there exist intermediate fields $K=K_{0}\subseteq K_{1}\subseteq \dots \subseteq K_{r}=L$ such that each $K_{i}$ is a simple radical extension of $K_{i-1}$: In other words, each $K_{i}$ is obtained by adjoining to $K_{i-1}$ a root of a polynomial of the form $x^{n}-a$.