Characteristic modules over a local ring
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916226701197312 |
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| author | Gheibi, Mohsen Takahashi, Ryo |
| author_facet | Gheibi, Mohsen Takahashi, Ryo |
| contents | Let $R$ be a commutative noetherian local ring, and let $M$ be a finitely generated $R$-module. Inspired by works of Vasconcelos and Briggs on characterization of complete intersection local rings through the homological properties of the conormal module, in this paper, we define the characteristic module $\mathrm{T}_M$ and the cocharacteristic module $\mathrm{E}_M$ of $M$, and investigate their properties. Our main results include characterizations of Cohen--Macaulay and Gorenstein local rings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_17680 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Characteristic modules over a local ring Gheibi, Mohsen Takahashi, Ryo Commutative Algebra 13D05, 13D07, 13H10 Let $R$ be a commutative noetherian local ring, and let $M$ be a finitely generated $R$-module. Inspired by works of Vasconcelos and Briggs on characterization of complete intersection local rings through the homological properties of the conormal module, in this paper, we define the characteristic module $\mathrm{T}_M$ and the cocharacteristic module $\mathrm{E}_M$ of $M$, and investigate their properties. Our main results include characterizations of Cohen--Macaulay and Gorenstein local rings. |
| title | Characteristic modules over a local ring |
| topic | Commutative Algebra 13D05, 13D07, 13H10 |
| url | https://arxiv.org/abs/2404.17680 |