发表机构
IMAR（罗马尼亚数学研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究单项式理想幂的相伴素的性质，建立K[x,y,z]中极大理想是否属于其相伴素集的准则，证明n≥3时存在无穷多理想的相伴素集波动，并构造不满足持久性等性质的理想例子。
AI 中文摘要
本文研究单项式理想幂的相伴素的性质，特别关注极大理想的存在性与波动现象。我们建立了判定K[x,y,z]中单项式理想幂的相伴素集中是否包含极大理想的准则，给出其在逐次幂的相伴素中出现与消失的例子。此外，我们证明对每个n≥3，K[x₁,…,xₙ]中存在无穷多单项式理想，其幂的相伴素集呈现波动现象。最后，我们构造了无穷多近无挠（或共近无挠）单项式理想的例子，这些理想不满足持久性（或共持久性）性质。
英文摘要
In this paper, we investigate the behavior of associated primes of powers of monomial ideals, with particular emphasis on the presence of the maximal ideal and the phenomenon of fluctuation. We establish criteria for determining when the maximal ideal belongs to the set of associated primes of powers of monomial ideals in $K[x,y,z]$, and provide examples illustrating its appearance and disappearance among the associated primes of successive powers. Furthermore, we prove that for every $n\geq 3$, there exist infinitely many monomial ideals in $K[x_1,\ldots,x_n]$ whose powers exhibit fluctuations in their sets of associated primes. Finally, we construct infinitely many examples of nearly normally torsion-free (respectively, co-nearly normally torsion-free) monomial ideals that fail to satisfy the persistence (respectively, copersistence) property.
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