\PassOptionsToPackage{main=italian}{babel} \documentclass[11pt]{scrartcl} \usepackage[sexy]{evan} \usepackage[utf8]{inputenc} \usepackage[italian]{babel} \usepackage{algorithm2e} \usepackage{amsfonts} \usepackage{amsthm} \usepackage{amssymb} \usepackage{amsopn} \usepackage{biblatex} \usepackage{bm} \usepackage{csquotes} \usepackage{mathtools} \usepackage{marvosym} \usepackage{tikz} \usepackage{wrapfig} \usepackage{xpatch} \addbibresource{bibliography.bib} \newcommand{\nsqrt}[2]{\!\sqrt[#1]{#2}\,} \newcommand{\card}[1]{\left|#1\right|} \newcommand{\zeroset}{\{0\}} \newcommand{\setminuszero}{\setminus \{0\}} \newcommand{\corref}[1]{\textit{Corollario \ref{#1}}} \newcommand{\exref}[1]{\textit{Esercizio \ref{#1}}} \newcommand{\exmplref}[1]{\textit{Esempio \ref{#1}}} \newcommand{\propref}[1]{\textit{Proposizione \ref{#1}}} \newcommand{\lemref}[1]{\textit{Lemma \ref{#1}}} \newcommand{\thref}[1]{\textit{Teorema \ref{#1}}} \newcommand{\BB}{\mathcal{B}} \newcommand{\HH}{\mathbb{H}} \newcommand{\KK}{\mathbb{K}} \newcommand{\ZZp}{\mathbb{Z}_p} \newcommand{\CCx}{\mathbb{C}[x]} \newcommand{\FFpp}{\mathbb{F}_p} \newcommand{\FFpd}{\mathbb{F}_{p^d}} \newcommand{\FFpm}{\mathbb{F}_{p^m}} \newcommand{\FFpn}{\mathbb{F}_{p^n}} \newcommand{\FFp}[1]{\mathbb{F}_{p^{#1}}} \newcommand{\KKx}{\mathbb{K}[x]} \newcommand{\QQx}{\mathbb{Q}[x]} \newcommand{\RRx}{\mathbb{R}[x]} \newcommand{\ZZi}{\mathbb{Z}[i]} \newcommand{\ZZom}{\mathbb{Z}[\omega]} \newcommand{\ZZpx}{\mathbb{Z}_p[x]} \newcommand{\ZZx}{\mathbb{Z}[x]} \renewcommand{\ii}{\mathbf{i}} \newcommand{\jj}{\mathbf{j}} \newcommand{\kk}{\mathbf{k}} \newcommand{\valalpha}{\varphi_\alpha} \newcommand{\Frob}{\mathcal{F}} \newcommand{\Frobexp}{\mathcal{F}{\mkern 1.5mu}} \newcommand{\dual}[1]{#1^{*}} \newcommand{\LL}[2]{\mathcal{L} \left(#1, \, #2\right)} \newcommand{\M}[1]{\mathcal{M}_{#1}\left(\KK\right)} \newcommand{\nsg}{\mathrel{\unlhd}} \renewcommand{\vec}[1]{\underline{#1}} \newcommand{\hatpi}{\hat{\pi}} \newcommand{\hatpip}{\hat{\pi}_p} \theoremstyle{definition} \DeclareMathOperator{\existsone}{\exists !} \DeclareMathOperator{\Imm}{Imm} \DeclareMathOperator{\MCD}{MCD} \DeclareMathOperator{\mcm}{mcm} \DeclareMathOperator{\tr}{tr} \let\oldemptyset\emptyset \let\emptyset\varnothing \let\oldcirc\circ \let\circ\undefined \DeclareMathOperator{\circ}{\oldcirc} \let\oldexists\exists \let\exists\undefined \DeclareMathOperator{\exists}{\oldexists} \let\oldforall\forall \let\forall\undefined \DeclareMathOperator{\forall}{\oldforall} \let\oldnexists\nexists \let\nexists\undefined \DeclareMathOperator{\nexists}{\oldnexists} \let\oldland\land \let\land\undefined \DeclareMathOperator{\land}{\oldland} \let\oldlnot\lnot \let\lnot\undefined \DeclareMathOperator{\lnot}{\oldlnot} \let\oldlor\lor \let\lor\undefined \DeclareMathOperator{\lor}{\oldlor} \setlength\parindent{0pt} \begin{document} \title{L'Algebrario} \subtitle{dispense del corso di Aritmetica} \author{Gabriel Antonio Videtta} \date{A.A. 2022/2023} \maketitle \thispagestyle{empty} \begin{center} \includegraphics[scale=0.3]{logo.png} \end{center} \newpage \thispagestyle{empty} ~\newpage \include{0. Premessa} \newpage \thispagestyle{empty} ~\newpage \tableofcontents \newpage \thispagestyle{empty} ~\newpage \include{1. Introduzione alla teoria degli anelli} \newpage \thispagestyle{empty} ~\newpage \include{2. Anelli euclidei, PID e UFD} \newpage \thispagestyle{empty} ~\newpage \include{3. Esempi notevoli di anelli euclidei} \newpage \thispagestyle{empty} ~\newpage \include{4. Proprietà fondamentali di Z[i], Zp[x], Z[x], Q[x]} \newpage \thispagestyle{empty} ~\newpage \include{5. Irriducibilità in Z[x] e Q[x]} \newpage \thispagestyle{empty} ~\newpage \include{6. Proprietà dei polinomi di K[x] e delle estensioni algebriche} \newpage \thispagestyle{empty} ~\newpage \include{7. Estensioni algebriche di K} \newpage \thispagestyle{empty} ~\newpage \include{8. Campi di spezzamento} \newpage \thispagestyle{empty} ~\newpage \include{9. Teorema fondamentale dell'algebra ed estensioni di Q} \newpage \thispagestyle{empty} ~\newpage \include{10. Teoremi rilevanti sui campi finiti} \newpage \thispagestyle{empty} ~\newpage \section{Riferimenti bibliografici} \printbibliography[heading=none] \end{document}