# Let $R = M_n(k)$, where $k$ is a field. Then any R-module that is finite dimensional over K is a direct sum of

Let $R = M_n(k)$, where $k$ is a field. Then any $R$-module that is finite dimensional over $K$ is a direct sum of isomorphic copies of $V$, where $V = k^n$.

I was able to show that $R$ has a unique simple module $V$, but I'm stuck on the rest of the exercise.

Any help is appreciated.

• Uh, what's the exercise? – user98602 Dec 14 '15 at 3:02
• I have edited for clarity. – 3-in-441 Dec 14 '15 at 3:25