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\begin{document}

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\begin{center}
{{\Large\bf ALGEBRA I}\\
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{\Large\bf HOMEWORK ASSIGNMENT VIII}\\
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{\bf (Turn in underlined problems.)}}
\end{center}

\vspace{.5in}

\noindent
{\bf 
\begin{tabbing}
\underline{\large\bf CHAPTER}\makebox[2in]{}\=\underline{\large\bf PROBLEMS}\\

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\noindent
7 \> \underline{7.24}, 7.25, \underline{7.28}, 7.29, 7.40

\end{tabbing}

}
\vspace{.5in}

\noindent
\underline{\large\bf ADDITIONAL PROBLEMS}
\vspace{.25in}

{\bf 

\underline{1.} Prove that any coboundary is a cocycle.

\bigskip

\underline{2.} 
Explicitly compute $H^2({\BZ}_2,{\BZ}_2,\theta)$.

\bigskip

3. Show that if $|Q|=n$, then $H^2(K,Q,\theta)$
satisfies $x^n = 1$.

\bigskip

4. Show that if $K$ satisfies $x^m=1$, then 
$H^2(K,Q,\theta)$ also satisfies $x^m = 1$.

\bigskip

\underline{5.} Assume that $\theta:{\BZ}_2\rightarrow K$
is constant. Show that $Z^2(K,{\BZ}_2,\theta)\cong K$.
Show that $B^2(K,{\BZ}_2,\theta)\cong 2K$.

\end{document}

