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 $x^n-a$.