Recall that a Gabriel filter of ideals $\mathscr{I}_\sigma$ of a commutative ring $R$ is a non–empty filter of ideals satisfying that every ideal $I$ of $R$, for which there exists an ideal $J\in\mathscr{I}_\sigma$ such that $(I : j):=\{r\in R\mid rj\in I\}\in\mathscr{I}_\sigma$ , for every $j\in J$, belongs to $\mathscr{I}_\sigma$. Now let $\mathscr{I}_\sigma$ be a Gabriel filter of ideals of a commutative ring $R$ such that $Nil(R)\in \mathscr{I}_\sigma$, where $Nil(R)=\{r\in R\mid r^n=0$ for some $n\in\mathbb{N}\}$. Can we deduced that $\langle 0\rangle\in\mathscr{I}_\sigma$?
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