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arXiv · 2609.00754

A counterexample to the localization problem for AB rings

Justin Lyle·Saeed Nasseh
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Abstract

We construct a complete local Gorenstein ring $R$ of dimension $1$ with a prime ideal $\mathfrak{p}\in \operatorname{Spec}(R)$ such that $R$ is an AB ring, but the localization $R_{\mathfrak{p}}$ 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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Justin Lyle, Saeed Nasseh. 2026-09-01. A counterexample to the localization problem for AB rings. https://arxiv.org/abs/2609.00754

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