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arXiv · 2609.14331

On the iso-Artinianness of one-dimensional Noetherian rings

Xiaolei Zhang·Ran Yan·Wei Qi
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Abstract

Let $R$ be a one-dimensional commutative Noetherian ring with a unique minimal prime $\mathfrak p$ such that $D=R/\mathfrak p$ is a principal ideal domain. We give a complete characterization of the iso-Artinian property in this class, that is, the following conditions are equivalent: $R$ is iso-Artinian; $\mathfrak pR_{\mathfrak p}=0$; $len_R(\mathfrak p)<\infty$; $\mathfrak p/\mathfrak p^2$ is torsion over $D$. As a consequence, we completely answer the Question~3.9 of Daneshvar and Divaani-Aazar: under their hypotheses $Min R\subsetneq Ass R$, the ring is iso-Artinian precisely when its nilradical has finite length, and it is non-iso-Artinian precisely when the conormal module has positive rank.

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Xiaolei Zhang, Ran Yan, Wei Qi. 2026-09-13. On the iso-Artinianness of one-dimensional Noetherian rings. https://arxiv.org/abs/2609.14331

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