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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2508.12237 |
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| _version_ | 1866912540844359680 |
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| author | Kosaka, Shinnosuke |
| author_facet | Kosaka, Shinnosuke |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_12237 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Characterizing Regular Local Rings via Analogues of (*)-properties Kosaka, Shinnosuke Commutative Algebra 13D02 (Primary), 13H10 (Secondary) 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. |
| title | Characterizing Regular Local Rings via Analogues of (*)-properties |
| topic | Commutative Algebra 13D02 (Primary), 13H10 (Secondary) |
| url | https://arxiv.org/abs/2508.12237 |