Example 31.2.7. Let $k$ be a field. The ring $R = k[x_1, x_2, x_3, \ldots ]/(x_ i^2)$ is local with locally nilpotent maximal ideal $\mathfrak m$. There exists no element of $R$ which has annihilator $\mathfrak m$. Hence $\text{Ass}(R) = \emptyset$, and $X = \mathop{\mathrm{Spec}}(R)$ is an example of a scheme which has no associated points.

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