Criteria for finite injective dimension of modules over a local ring
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866909573762252800 |
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| author | Kosaka, Shinnosuke Mifune, Yuki Shimizu, Kenta |
| author_facet | Kosaka, Shinnosuke Mifune, Yuki Shimizu, Kenta |
| contents | Let $R$ be a commutative Noetherian local ring. We prove that the finiteness of the injective dimension of a finitely generated $R$-module $C$ is determined by the existence of a Cohen--Macaulay module $M$ that satisfies an inequality concerning multiplicity and type, together with the vanishing of finitely many Ext modules. As applications, we recover a result of Rahmani and Taherizadeh and provide sufficient conditions for a finitely generated $R$-module to have finite injective dimension. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_07536 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Criteria for finite injective dimension of modules over a local ring Kosaka, Shinnosuke Mifune, Yuki Shimizu, Kenta Commutative Algebra 13D05, 13D07, 13H10 Let $R$ be a commutative Noetherian local ring. We prove that the finiteness of the injective dimension of a finitely generated $R$-module $C$ is determined by the existence of a Cohen--Macaulay module $M$ that satisfies an inequality concerning multiplicity and type, together with the vanishing of finitely many Ext modules. As applications, we recover a result of Rahmani and Taherizadeh and provide sufficient conditions for a finitely generated $R$-module to have finite injective dimension. |
| title | Criteria for finite injective dimension of modules over a local ring |
| topic | Commutative Algebra 13D05, 13D07, 13H10 |
| url | https://arxiv.org/abs/2504.07536 |