Abstract:Let $I$ be an ideal in a commutative Noetherian ring $R$. We say that a positive integer $\ell_0$ is the strong persistence index of $I$ if $\ell_0$ is the smallest integer such that $(I^{\ell+1} :_R I) = I^{\ell}$ for all $\ell \geq \ell_0$. The first aim of this paper is to study this notion for monomial ideals.
We also introduce the notion of fluctuation in colon powers if there exist positive integers $a < b < c$ such that at least one of the following cases occurs:
(i) $(I^{a} : I) = I^{a-1}$, $(I^{b} : I) \neq I^{b-1}$, but $(I^{c} : I) = I^{c-1}$.
(ii) $(I^{a} : I) \neq I^{a-1}$, $(I^{b} : I) = I^{b-1}$, but $(I^{c} : I) \neq I^{c-1}$.
The second purpose of this work is to study this phenomenon for monomial ideals.
| Comments: | This paper has been published in Mathematics 2026, 14(10), 1705. (this https URL) |
| Subjects: | Commutative Algebra (math.AC) |
| Cite as: | arXiv:2604.11475 [math.AC] |
| (or arXiv:2604.11475v2 [math.AC] for this version) | |
| https://doi.org/10.48550/arXiv.2604.11475 arXiv-issued DOI via DataCite |
From: Mehrdad Nasernejad [view email]
[v1]
Mon, 13 Apr 2026 13:45:05 UTC (14 KB)
[v2]
Fri, 22 May 2026 09:41:27 UTC (17 KB)
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