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\Huge{Reading Quiz \S16}
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\normalsize

\begin{enumerate}
\item $[2]$ Give an example of a ring.  Clearly state the binary operators. 
\vfill
\item Let $R$ be a ring with binary operators $+$, and $\cdot$.  Determine whether the following statements are \emph{always} true or false.  If false, provide a counterexample, that is, name a ring that does not satisfy the statement.
\begin{enumerate}

\item $[1]$ If $x$, $y \in R$,  then $x+y= y+x$.
\vfill
\item $[1]$ If $x$, $y \in R$, then $x\cdot y= y\cdot x$.
\vfill
\end{enumerate}



\item $[1]$ Let $R$ be a commutative ring with unity.  Furthermore, say $R$ is such that every nonzero element has an inverse.  $R$ is a ring (and an abelian group-twice over), but what other algebraic structure is $R$?
 \vfill

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