Math 6310 • Algebra

Let \(R\) be an infinite simple ring (i.e., a ring with infinitely many elements and with no
2-sided ideals except \(\{0\}\) and \(R\)). Show that exactly one of the following holds.
\begin{enumerate}
\item[(a)] \(R\) is a division ring.
\item[(b)] \(R\) has an infinite number of right ideals.
\end{enumerate}