\(\renewcommand{\QQ}{\mathbb{Q}} \renewcommand{\ZZ}{\mathbb{Z}} \renewcommand{\RR}{\mathbb{R}} \renewcommand{\FF}{\mathbb{F}} \renewcommand{\CC}{\mathbb{C}} \renewcommand{\HH}{\mathbb{H}} \renewcommand{\QQbar}{\bar{\QQ}} \renewcommand{\barQQ}{\bar{\QQ}} \renewcommand{\Fpbar}{\bar{\FF}_p} \renewcommand{\cC}{\mathcal{C}} \renewcommand{\fX}{\mathfrak{X}} \renewcommand{\SL}{\operatorname{SL}} \renewcommand{\GL}{\operatorname{GL}} \renewcommand{\PSL}{\operatorname{PSL}} \renewcommand{\PGL}{\operatorname{PGL}} %Some common abreviations \renewcommand{\lto}{\longrightarrow} \renewcommand{\dfn}{\ensuremath{:=}} \renewcommand{\surjects}{\twoheadrightarrow} \renewcommand{\injects}{\hookrightarrow} \renewcommand{\id}{\operatorname{Id}} \renewcommand{\tns}[1][]{\otimes_{\!#1}} \renewcommand{\mtx}[4]{\left(\begin{matrix}#1\\#3\end{matrix}\right)} \renewcommand{\mat}[1]{\left(\begin{matrix}#1\end{matrix}\right)} \renewcommand{\smat}[1]{\left(\begin{smallmatrix}#1\end{smallmatrix}\right)} \renewcommand{\smtx}[4]{\left(\begin{smallmatrix}#1\\#3\end{smallmatrix}\right)} \renewcommand{\slz}{\operatorname{SL}_2(\bZ)} \renewcommand{\to}{\longrightarrow} \renewcommand{\dlog}{\operatorname{dlog}} % \renewcommand{\Im}{\operatorname{Im}} % \renewcommand{\Re}{\operatorname{Re}} \renewcommand{\abs}[1]{|#1|} \renewcommand{\slsh}[1]{|_{#1}} \renewcommand{\qed}{\blacksquare} \renewcommand{\Irr}{\operatorname{Irr}} \renewcommand{\Aut}{\operatorname{Aut}} \renewcommand{\Gal}{\operatorname{Gal}} \renewcommand{\Mor}{\operatorname{Mor}} \renewcommand{\Hom}{\operatorname{Hom}} % \renewcommand{\implies}{\Longrightarrow} % \renewcommand{\char}{\operatorname{char}} \renewcommand{\car}{\operatorname{char}} \renewcommand{\mcd}{\operatorname{mcd}} \renewcommand{\gcd}{\operatorname{mcd}} \renewcommand{\Eq}{\operatorname{Eq}} \renewcommand{\res}{\operatorname{res}} \renewcommand{\normaleq}{\trianglelefteq} \renewcommand{\disc}{\operatorname{disc}}\)

Bibliografia

1.

Artin Michael (2014) Algebra / Michael Artin., 2nd ed., new international ed. Pearson, Edinbourgh Gate, Harlow, Essex

2.

Dummit DS, Foote RM (2004) Abstract algebra, 3rd ed. Wiley, New York

3.

Geck M (2014) On the characterization of Galois extensions. Amer Math Monthly 121:637-639. doi: 10.4169/amer.math.monthly.121.07.637

4.

Jelonek Z (1993) A simple proof of the existence of the algebraic closure of a field. Univ Iagel Acta Math 131-132

5.

Rotman JJ (2015) Advanced modern algebra. Part 1, Third. American Mathematical Society, Providence, RI

6.

Weintraub SH (2021) The theorem of the primitive element. Amer Math Monthly 128:753-754. doi: 10.1080/00029890.2021.1944757