The following Daily Questions were asked this week.

Tuesday, June 6

First Question

By definition, a field extension $F\subseteq E$ is a root extension if …

Reveal Answer

Answer

… there exists a chain of intermediate extensions $F=F_0\subseteq F_1\subseteq F_2\subseteq \cdots \subseteq F_r = E$ with each extension $F_i\subseteq F_{i+1}$ a simple radical extension, i.e., with $F_{i+1}=F_i(\sqrt[n_i]{a_i})$ for some $a_i\in F_i$.

Second Question

By definition, an element $\alpha\in \overline{F}$ can be expressed by radicals if …

Reveal Answer

Answer

… it is contained in some root extension $F\subseteq E$.