%        File: hw1.tex
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\begin{document}
\begin{center}
    \textsc{Math 4140/5140. Homework 11}\\
    due Friday, April 29
\end{center}

\vspace{1em}

\noindent\textbf{Note:} All numbered exercises are from Erdmann--Holm ([EH]).\\

\begin{enumerate}
\item Read Section 3.4.3 of [EH], which explains
    why every simple module of a direct product of algebras is isomorphic
    to the inflation of a simple module of some factor in the
    product. 
\item Read Sections 6.1 and 6.2 of [EH]. 
\item In the notes for Lecture 35 (April 15), we proved that the map $\Phi$
     from the lecture is a surjective algebra homomorphism. Using the notation
     there, finish the proof that $\Phi$ is an algebra isomorphism.
\item Exercise 5.4. 
\item Exercise 6.4. 
%\item Exercise 6.5. 
\item Exercise 6.9. 

\end{enumerate} 
\end{document}


