\contentsline {section}{\numberline {1}Preliminari}{1}{section.1}
\contentsline {section}{\numberline {2}Estensione di Campi}{3}{section.2}
\contentsline {subsection}{\numberline {2.1}Caratteristica}{3}{subsection.2.1}
\contentsline {subsection}{\numberline {2.2}Estensioni}{6}{subsection.2.2}
\contentsline {subsection}{\numberline {2.3}Campi di spezzamento}{12}{subsection.2.3}
\contentsline {subsection}{\numberline {2.4}Campi chiusi e chiusura}{14}{subsection.2.4}
\contentsline {section}{\numberline {3}Campi finiti}{16}{section.3}
\contentsline {subsection}{\numberline {3.1}Estensioni separabili}{17}{subsection.3.1}
\contentsline {section}{\numberline {4}Polinomi simmetrici}{20}{section.4}
\contentsline {section}{\numberline {5}Estensioni normali}{22}{section.5}
\contentsline {section}{\numberline {6}Gruppo di Galois}{23}{section.6}
\contentsline {subsection}{\numberline {6.1}Teorema fondamentale dell'algebra}{29}{subsection.6.1}
\contentsline {subsection}{\numberline {6.2}Estensioni ciclotomiche}{30}{subsection.6.2}
\contentsline {subsection}{\numberline {6.3}Riga e compasso}{31}{subsection.6.3}
\contentsline {subsubsection}{\numberline {6.3.1}Ciclotomia}{32}{subsubsection.6.3.1}
\contentsline {section}{\numberline {7}Gruppi risolubili}{33}{section.7}
\contentsline {subsection}{\numberline {7.1}Risolubilita' di Sn}{33}{subsection.7.1}
\contentsline {subsection}{\numberline {7.2}Estensioni risolubili}{34}{subsection.7.2}
\contentsline {subsection}{\numberline {7.3}Estensioni risolubili per radicali}{36}{subsection.7.3}
\contentsline {section}{\numberline {8}*}{37}{section.8}