Radical property of the traces of the canonical modules of Cohen-Macaulay rings
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915354824933376 |
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| author | Miyazaki, Mitsuhiro |
| author_facet | Miyazaki, Mitsuhiro |
| contents | In this paper, we define a new concept of Noetherian commutative rings which stands between Gorenstein and Cohen-Macaulay properties. We show that this new property keep hold under common operations of commutative rings such as localization, polynomial extension and under mild assumptions, flat extension, tensor product, Segre product and so on. We show that for Schubert cycles, the Ehrhart rings of cycle graphs and perfect graphs, this new concept is close to Gorenstein property. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_17987 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Radical property of the traces of the canonical modules of Cohen-Macaulay rings Miyazaki, Mitsuhiro Commutative Algebra 13H10, 14M15, 05E40, 05C25, 52B20 In this paper, we define a new concept of Noetherian commutative rings which stands between Gorenstein and Cohen-Macaulay properties. We show that this new property keep hold under common operations of commutative rings such as localization, polynomial extension and under mild assumptions, flat extension, tensor product, Segre product and so on. We show that for Schubert cycles, the Ehrhart rings of cycle graphs and perfect graphs, this new concept is close to Gorenstein property. |
| title | Radical property of the traces of the canonical modules of Cohen-Macaulay rings |
| topic | Commutative Algebra 13H10, 14M15, 05E40, 05C25, 52B20 |
| url | https://arxiv.org/abs/2506.17987 |