Radical extension

In mathematics and more specifically in field theory, a radical extension of a field K is an extension of K that is obtained by adjoining a sequence of nth roots of elements.

A simple radical extension is a simple extension F/K generated by a single element α satisfying ${\displaystyle \alpha ^{n}=b}$ for an element b of K. In characteristic p, we also take an extension by a root of an Artin–Schreier polynomial to be a simple radical extension. A radical series is a tower ${\displaystyle K=F_{0}<F_{1}<\cdots <F_{k}}$ where each extension ${\displaystyle F_{i}/F_{i-1}}$ is a simple radical extension.

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