This analysis establishes a criterion for regular local rings using various properties, suggesting important refinements to previous frameworks.
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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Shinnosuke Kosaka (2025) studied this question.
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