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\title{Math 724\\Summer 2010\\Homework 3}
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\centerline{\it Due Monday, August 2, 2010.}

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\noindent 1. (5 pt) Let $R$ be a domain with quotient field $K$ and $I, J, L$ fractional ideals of $R$.
\begin{enumerate}
\item (5 pt) Show that if $I$ is divisorial, then so is $I:J$.
\item (5 pt) Show that $I:JL=(I:J):L$.
\item (5 pt) Show that $(I:J)L\subseteq I:(J:L)$.
\item (5 pt) Show that $R:((R:I)I)=(R:I):(R:I)$
\end{enumerate}

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\noindent 2. (5 pt) Show that if $I\subseteq R$ is an ideal that is maximal with respect to being divisorial, then $I$ is prime.

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