We prove that the integral closure of a strongly Golod ideal in a polynomial ring over a field of characteristic zero is strongly Golod, positively answering a question of Huneke. More generally, the rational power $I_{\unicode[STIX]{x1D6FC}}$ of an arbitrary homogeneous ideal is strongly Golod for $\unicode[STIX]{x1D6FC}\geqslant 2$ and, if $I$ is strongly Golod, then $I_{\unicode[STIX]{x1D6FC}}$ is strongly Golod for $\unicode[STIX]{x1D6FC}\geqslant 1$. We also show that all the coefficient ideals of a strongly Golod ideal are strongly Golod.

中文翻译：

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强烈黄金理想的整体封闭

我们证明了在特征为零的域上多项式环中强 Golod 理想的积分闭包是强 Golod，从而肯定地回答了 Huneke 的问题。更一般地说，理性权力$I_{\unicode[STIX]{x1D6FC}}$任意齐次理想的强烈戈洛德$\unicode[STIX]{x1D6FC}\geqslant 2$而如果$I$是强烈的黄金，那么$I_{\unicode[STIX]{x1D6FC}}$非常适合$\unicode[STIX]{x1D6FC}\geqslant 1$. 我们还表明，强 Golod 理想的所有系数理想都是强 Golod。