关于单项式理想的微分幂滤过的F - 阈值
On $F$-thresholds of differential power filtrations
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中文总结 AI 辅助
研究单项式理想的微分幂滤过的F - 阈值，给出其存在性及上界，应用结果表明多项式环维数与单项式极大理想的该滤过F - 阈值相同。
中文摘要 AI 辅助
我们研究单项式理想的微分幂滤过的F - 阈值。给出了该数的存在性，并表明它以上述单项式理想的极小素理想的最大高度为上界。作为结果的应用，我们证明了多项式环的维数与单项式极大理想的微分幂滤过的F - 阈值相同。
英文摘要
We study the $F$-threshold of differential power filtrations of monomial ideals. We give the existence of this number and show that it is upper bounded by the maximum height of the minimal primes of the underlying monomial ideal. As an application of our results, we show that the dimension of the polynomial ring and the $F$-threshold of the differential power filtration of the monomial maximal ideal are the same.
