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I faced the following problem but I do not know how to solve it. Please help me. Thanks.

Let $R$ is a Noetherian graded ring and $I$ is an ideal of $R$, $I^*$ be the ideal generated by all the homogeneous element contained in $I$. Prove that $\operatorname{ht}(I)-1\le\operatorname{ht}(I^{*})\le\operatorname{ht}(I)$.

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closed as too localized by Qiaochu Yuan Jun 3 '12 at 19:51

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Can you include the definition of $I^*$? –  Martin Brandenburg May 22 '12 at 17:51
I think $I^*$ is the ideal of $R$ generated by all homogeneous elements contained in $I$. –  Arsenaler May 23 '12 at 0:45

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