\contentsline {section}{\numberline {1}Preliminari}{1}{section.1}
\contentsline {section}{\numberline {2}Estensione di Campi}{8}{section.2}
\contentsline {subsection}{\numberline {2.1}Caratteristica}{8}{subsection.2.1}
\contentsline {subsection}{\numberline {2.2}Estensioni}{15}{subsection.2.2}
\contentsline {subsection}{\numberline {2.3}Campi di spezzamento}{34}{subsection.2.3}
\contentsline {subsection}{\numberline {2.4}Campi chiusi e chiusura}{42}{subsection.2.4}
\contentsline {section}{\numberline {3}Campi finiti}{50}{section.3}
\contentsline {subsection}{\numberline {3.1}Proprieta' di $x^{p^n}-x$}{55}{subsection.3.1}
\contentsline {subsection}{\numberline {3.2}Estensioni separabili}{58}{subsection.3.2}
\contentsline {section}{\numberline {4}Polinomi simmetrici}{69}{section.4}
\contentsline {section}{\numberline {5}Estensioni normali}{74}{section.5}
\contentsline {section}{\numberline {6}Gruppo di Galois}{78}{section.6}
\contentsline {subsection}{\numberline {6.1}Teorema fondamentale dell'algebra}{107}{subsection.6.1}
\contentsline {subsection}{\numberline {6.2}Estensioni ciclotomiche}{111}{subsection.6.2}
\contentsline {subsection}{\numberline {6.3}Riga e compasso}{119}{subsection.6.3}
\contentsline {subsubsection}{\numberline {6.3.1}Ciclotomia}{132}{subsubsection.6.3.1}
\contentsline {section}{\numberline {7}Gruppi risolubili}{139}{section.7}
\contentsline {subsection}{\numberline {7.1}Risolubilita' di Sn}{145}{subsection.7.1}
\contentsline {subsection}{\numberline {7.2}Estensioni risolubili}{146}{subsection.7.2}
\contentsline {subsection}{\numberline {7.3}Estensioni risolubili per radicali}{158}{subsection.7.3}
\contentsline {subsection}{\numberline {7.4}Discriminante}{166}{subsection.7.4}
\contentsline {section}{\numberline {8}Esercizi}{170}{section.8}
\contentsline {section}{\numberline {9}*}{186}{section.9}