\documentclass[10pt]{amsart}
\input colin.sty
%\input thmsty.sty
\input epsf.sty
\usepackage{epic,eepic}
\usepackage{graphics,color}
%\pagestyle{empty}
%\oddsidemargin 0pt
%\textwidth 6.5in
%\textheight 9.5in
%\topmargin -.5in
\usepackage{multicol}

\begin{document}

%\begin{frame}
%\titlepage
%\frametitle{}

\centerline{\bf \large  11.2}

\bt (Theorem 11.6) Let $K$ be an extension field of $F$ and $u\in K$ algebraic over $F.$ Then there is a \red{\bf unique}, \blue{\bf monic}, \purple{\bf irreducible} polynomial $p(x)\in F[x]$ that has $u$ as a root. Furthermore, if $u$ is a root of $g(x)\in F[x],$ then $p(x)\mid g(x).$
\et

\bt (Theorem 11.7) Let $K$ be an extension field of $F$ and $u\in K$ algebraic over $F$ with minimal polynomial $p(x)$ of degree $n.$ Then
\be \item $F(u)\cong F[x]/(p(x))$
    \item $\{1, u, u^2, \ldots, u^{n-1}\}$ is a basis of $F(u)$ over $F.$
    \item $[F(u):F]=n$
    \item $F[u]=F(u)$
\ee




\end{document}
