# Annihilator of the maximal ideal of a uniserial ring

Recently while reading a paper I encounter a problem, which has confused me for several days. So I hope that some one could help. Thanks for your attention. My problem is: let $R$ be a commutative uniserial ring(i.e., its set of ideals is totally ordered by inclusion), $m$ denotes its unique maximal ideal and Ann(m) denotes the annihilator of $m$. Then $Ann(m/Ann(m))=0$ when $m/Ann(m)$ is treated as the maximal ideal of $R/Ann(m)$.

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Perhaps I'm confused. If $R = k[t]/(t^5)$, then the annihilator of the maximal ideal $(t)$ is $t^4$, but the annihlator of $(t)/(t^4)$ in $R/(t^4)$ is not zero. – Graham Leuschke Sep 18 '10 at 2:01
Thanks, Graham. Your example is correct. – TmobiusX Sep 19 '10 at 6:24