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arXiv · 2508.12237

Characterizing Regular Local Rings via Analogues of (*)-properties

Shinnosuke Kosaka
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Abstract

Let $R$ be a commutative noetherian local ring. As analogues of $(*)$-properties introduced by Ghosh, Gupta, and Puthenpurakal, we introduce and study $(\mathrm{A})$-properties, $(\mathrm{B})$-properties, and $(\mathrm{C})$-relations. Using these three notions, we establish a criterion for a local ring to be regular. This recovers and refines the main result of Ghosh, Gupta, and Puthenpurakal and has further applications.

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Shinnosuke Kosaka. 2025-08-17. Characterizing Regular Local Rings via Analogues of (*)-properties. https://arxiv.org/abs/2508.12237

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