Annihilator of local cohomology modules under localization and completion
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866908509004627968 |
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| author | Hang, Nguyen Thi Anh Nhan, Le Thanh |
| author_facet | Hang, Nguyen Thi Anh Nhan, Le Thanh |
| contents | Let $(R, \frak m)$ be a Noetherian local ring. This paper deals with the annihilator of Artinian local cohomology modules $H^i_{\frak m}(M)$ in the relation with the structure of the base ring $R$, for non negative integers $i$ and finitely generated $R$-modules $M$. Firstly, the catenarity and the unmixedness of local rings are characterized via the compatibility of annihilator of top local cohomology modules under localization and completion, respectively. Secondly, some necessary and sufficient conditions for a local ring being a quotient of a Cohen-Macaulay local ring are given in term of the annihilator of all local cohomology modules under localization and completion. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_06280 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Annihilator of local cohomology modules under localization and completion Hang, Nguyen Thi Anh Nhan, Le Thanh Commutative Algebra 13D45, 13H10, 13E05 Let $(R, \frak m)$ be a Noetherian local ring. This paper deals with the annihilator of Artinian local cohomology modules $H^i_{\frak m}(M)$ in the relation with the structure of the base ring $R$, for non negative integers $i$ and finitely generated $R$-modules $M$. Firstly, the catenarity and the unmixedness of local rings are characterized via the compatibility of annihilator of top local cohomology modules under localization and completion, respectively. Secondly, some necessary and sufficient conditions for a local ring being a quotient of a Cohen-Macaulay local ring are given in term of the annihilator of all local cohomology modules under localization and completion. |
| title | Annihilator of local cohomology modules under localization and completion |
| topic | Commutative Algebra 13D45, 13H10, 13E05 |
| url | https://arxiv.org/abs/2412.06280 |