Define $ Jac(R) = \cap_{\mathfrak{m}, maximal } \mathfrak{m}$ and $Nil(R) = \cap_{\mathfrak{p}, prime} \mathfrak{p}$, where $R$ is a commutative ring. Can someone give me an example of a commutative ring $R$ such that $Jac(R) \ne Nil(R)$. I have ruled out $\mathbb{Z}_{n}, \mathbb{Z}$, and any Art...