Abstract Powers of (monomial) ideals is a subject that still calls attraction in various ways. Let be a monomial ideal and let G(I) denote the (unique) minimal monomial generating set of I. How small can be in terms of ? Until recently, it was widely expected that would always hold. The first counterexamples emerged in 2018 for n = 2. In this article we show that for any n and d there is an -primary monomial ideal such that for all

中文翻译：

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在任意数量的变量中具有任意高的微小幂的单项式理想

（单项式）理想的抽象力量是一个仍然以各种方式称为吸引力的主题。设一个单项式理想，让 G(I) 表示 I 的（唯一的）最小单项式生成集。 就 而言可以有多小？直到最近，人们普遍预计这将永远成立。n = 2 的第一个反例出现在 2018 年。 在本文中，我们表明对于任何 n 和 d 都存在一个 -primary 单项式理想，使得对于所有