If $R$ is a local ring and $M$ and $N$ are finitely generated R-modules such that $M\otimes N = 0$ then it follows from Nakayama's lemma that either $M=0$ or $N=0$. This I know. But now
I am looking for an example of a local ring $R$ and two modules $M,N$ such that $M\otimes N = 0$ but neither $M=0$ nor $N=0$.
Thanks