Let $S$ be a graded ring generated by finite elements of $S_1$ as $S_0$-algebra and let $M$ be a graded $S$-module. For $m \in M$, if $m=0$ in $M_f$ for all generators $f \in S_1$, then $m=0$?
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No, a counterexample is $M=S/S_+=S_0$.
Martin Brandenburg
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Then, Martin... for large enough $d$, if $m \in M_d$, it is true?? – Sang Cheol Lee May 02 '13 at 02:03