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\begin{document}

\title{Math 101: Graduate Linear Algebra \\ Daily Homework \#20}
\date{Assigned Wednesday, 25 October 2017; due Friday, 27 October 2017}

\maketitle

\vspace{1ex}

\begin{problab}{20.1} 
Let $R=\R[x,y,z]/(xy-z^2)$.  Let $P=(\overline{x},\overline{z})$ be the ideal generated by the images of $x,z$ in $R$.  
\begin{enumalph}
\item Show that $P$ is prime.
\item Let $R_P$ be the localization of $R$ at $P$.  Prove that $P^2 R_P \cap R = (\overline{x})$.  Note that this ideal is \emph{bigger} than $P^2$.
\end{enumalph}
\end{problab}

\end{document}