Math 6310 • Algebra

\begin{enumerate}
\item[(a)] Let \(R\) be a ring and let \(M\) be an \(R\)-module. Prove that if \(M\) is generated by
simple submodules, then \(M\) is the direct sum of simple submodules.
\item[(b)] Show that every vector space over a field has a basis.
\end{enumerate}