\documentclass[11pt,a4paper]{article}
\usepackage[T1]{fontenc}
\usepackage{isabelle,isabellesym}
\usepackage{amssymb}
\usepackage{pdfsetup}
\urlstyle{rm}
\isabellestyle{it}

\begin{document}

\title{Finite Fields}
\author{Emin Karayel}
\maketitle

\abstract{This entry formalizes the classification of the finite fields (also called Galois fields):
For each prime power $p^n$ there exists exactly one (up to isomorphisms) finite field of that size
and there are no other finite fields.
The derivation includes a formalization of the characteristic of rings, the Frobenius endomorphism, 
formal differentiation for polynomials in HOL-Algebra and Gauss' formula for the number of
monic irreducible polynomials over finite fields:
\[
\frac{1}{n} \sum_{d | n} \mu(d) p^{n/d} \textrm{.}
\]
The proofs are based on the books from Ireland and Rosen~\cite{ireland1982}, as well as,
Lidl and Niederreiter~\cite{lidl1986}.
}
  
\parindent 0pt\parskip 0.5ex

\tableofcontents

\input{session}

\bibliographystyle{abbrv}
\bibliography{root}

\end{document}