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September 24, 2025Open Access

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

Key Points

Establishing a clear criterion for identifying regular local rings enhances understanding in algebra.
The study introduces (A)-properties, (B)-properties, and (C)-relations to characterize these rings.
This research builds upon and refines earlier results from Ghosh, Gupta, and Puthenpurakal.
Applications extend beyond theoretical contributions, impacting further algebraic studies.

Abstract

Let R be a commutative noetherian local ring. As analogues of (*) -properties introduced by Ghosh, Gupta, and Puthenpurakal, we introduce and study (A) -properties, (B) -properties, and (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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Cite This Study

Shinnosuke Kosaka (Sun,) studied this question.

synapsesocial.com/papers/68d6e1978b2b6861e4c404ed https://doi.org/https://doi.org/10.48550/arxiv.2508.12237

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