notes/Aritmetica/aritmetica.tex

\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}