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\title{Problem Set \#3}

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\section*{Book Problems}

2, 13a, 13d, 13e, 28, 36, 37, 50, 51

\section*{Extra Problems}

\begin{enumerate}
\item State, prove, and explain the two versions of the Chinese Remainder theorem used in the book.
\item If $f, g\colon R\to S$ are ring homomorphism, prove that 
\[
ker(f-g)=\{r | (f-g)(r)=0\}
\] is a ring. If $R$ and $S$ are unital, then show that this ring is also unital.

For extra credit, you can show that the ring you get is a pull-back in the category of [unital] rings.
\end{enumerate}

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