Example 10.68.3. Let $k$ be a field. Consider the ring $k[x, y, w_0, w_1, w_2, \ldots ]/I$ where $I$ is generated by $yw_ i$, $i = 0, 1, 2, \ldots$ and $w_ i - xw_{i + 1}$, $i = 0, 1, 2, \ldots$. The sequence $x, y$ is regular, but $y$ is a zerodivisor. Moreover you can localize at the maximal ideal $(x, y, w_ i)$ and still get an example.

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