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On the iso-Artinianness of one-dimensional Noetherian rings
Abstract
Let R be a one-dimensional commutative Noetherian ring with a unique minimal prime p such that D=R/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; pRp=0; lenR(p)<∞; p/p2 is torsion over D. As a consequence, we completely answer the Question~3.9 of Daneshvar and Divaani-Aazar: under their hypotheses Min Rsubsetneq 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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BibTeX
@misc{zhang2026isoartinianness,
title = {{On the iso-Artinianness of one-dimensional Noetherian rings}},
author = {Xiaolei Zhang and Ran Yan and Wei Qi},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.14331},
eprint = {2609.14331},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.14331},
}
RIS
TY - UNPB
TI - On the iso-Artinianness of one-dimensional Noetherian rings
AU - Xiaolei Zhang
AU - Ran Yan
AU - Wei Qi
PY - 2026
DA - 2026/09/13
PB - arXiv
DO - 10.48550/arxiv.2609.14331
UR - https://arxiv.org/abs/2609.14331
AB - Let R be a one-dimensional commutative Noetherian ring with a unique minimal prime p such that D=R/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; pR_p=0; len_R(p)<∞; p/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 Rsubsetneq 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.
ER -