Show a module is simple Let $M$ be a non-zero module and suppose that every non-zero module homomorphism $f:M\rightarrow N$ is injective. Show that $M$ is simple. 
My idea is to let $N$ be a submodule; then pick a map to show it must be zero or $M$. 
Thanks

You are on the right track. Choose $N$ to be a submodule, and take $f:M \rightarrow M/N$ to be the quotient map. Can you proceed now?
