Author

Saeed Nasseh

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Preprint Sep 2026

A counterexample to the localization problem for AB rings

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.

Justin Lyle, Saeed Nasseh · 0 citations