论文标题
强烈的持久性和相关的单一理想力量
Strong persistence and associated prime of powers of monomial ideals
论文作者
论文摘要
令$ r = k [x_1，\ ldots，x_n] $为$ n $变量$ k $的$ n $变量，而$ i $是$ d \ d \ leq 2 $的单一理想。我们表明，$（i^{k+1}：i）= i^k $ for hast $ k \ geq 1 $，我们反驳了一个动机问题，该问题出现在\ cite [Question 2.51] {chhv}中，通过提供反例。同样，在这个反例中，我们对以下问题给出了负面答案，即无正方形的单一理想的深度功能是非侵扰的。
Let $R=K[x_1,\ldots, x_n]$ be the polynomial ring in $n$ variables over a field $K$ and $I$ be a monomial ideal of degree $d\leq 2$. We show that $(I^{k+1}:I)=I^k$ for all $k\geq 1$ and we disprove a motivation question that was appeared in \cite[Question 2.51]{CHHV} by providing of a counterexample. Also, by this counterexample, we give a negative answer to the question that depth function of square-free monomial ideals are non-increasing.
