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A counterexample to the localization problem for AB rings
Abstract
We construct a complete local Gorenstein ring R of dimension $1$ with a prime ideal p∈ Spec(R) such that R is an AB ring, but the localization Rp is not an AB ring. This settles the localization problem for AB rings posed by Huneke and Jorgensen in the negative.
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BibTeX
@misc{lyle2026counterexample,
title = {{A counterexample to the localization problem for AB rings}},
author = {Justin Lyle and Saeed Nasseh},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.00754},
eprint = {2609.00754},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.00754},
}
RIS
TY - UNPB
TI - A counterexample to the localization problem for AB rings
AU - Justin Lyle
AU - Saeed Nasseh
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.00754
UR - https://arxiv.org/abs/2609.00754
AB - We construct a complete local Gorenstein ring R of dimension $1$ with a prime ideal p∈ Spec(R) such that R is an AB ring, but the localization R_p is not an AB ring. This settles the localization problem for AB rings posed by Huneke and Jorgensen in the negative.
ER -