INTEGRAL CLOSURE OF STRONGLY GOLOD IDEALS
INTEGRAL CLOSURE OF STRONGLY GOLOD IDEALS
复制标题
强烈的金理想的整体封闭
DOI：
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发表时间：
2019
影响因子：
0.8
通讯作者：
Cătălin Ciupercă
中科院分区：
文献类型：
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作者：
Cătălin Ciupercă
我们证明了多项式环中特征零域上的强戈洛德理想的积分闭包是强戈洛德，正面回答了胡内克的问题。更一般地，任意齐次理想的有理幂 $I_{unicode[STIX]{x1D6FC}}$ 对于 $unicode[STIX]{x1D6FC}geqslant 2$ 是强戈洛德，并且，如果 $I$ 是强戈洛德，则 $I_{unicode[STIX]{x1D6FC}}$ 对于 $unicode[STIX]{x1D6FC}geqslant 1$ 是强戈洛德。我们还证明，强戈洛德理想的所有系数理想都是强戈洛德理想。
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.