Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Lyle, Justin, Nasseh, Saeed
Institutions: Georgia Southern University, Auburn University
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Auburn University
OpenAlex ID: W7206189591