Auslander-Reiten conjecture and finite injective dimension of Hom
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arXiv
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866910311611629568 |
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| author | Ghosh, Dipankar Takahashi, Ryo |
| author_facet | Ghosh, Dipankar Takahashi, Ryo |
| contents | For a finitely generated module $ M $ over a commutative Noetherian ring $R$, we settle the Auslander-Reiten conjecture when at least one of ${\rm Hom}_R(M,R)$ and ${\rm Hom}_R(M,M)$ has finite injective dimension. A number of new characterizations of Gorenstein local rings are also obtained in terms of vanishing of certain Ext and finite injective dimension of Hom. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2109_00692 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Auslander-Reiten conjecture and finite injective dimension of Hom Ghosh, Dipankar Takahashi, Ryo Commutative Algebra Primary 13D07, 13D05, 13H10 For a finitely generated module $ M $ over a commutative Noetherian ring $R$, we settle the Auslander-Reiten conjecture when at least one of ${\rm Hom}_R(M,R)$ and ${\rm Hom}_R(M,M)$ has finite injective dimension. A number of new characterizations of Gorenstein local rings are also obtained in terms of vanishing of certain Ext and finite injective dimension of Hom. |
| title | Auslander-Reiten conjecture and finite injective dimension of Hom |
| topic | Commutative Algebra Primary 13D07, 13D05, 13H10 |
| url | https://arxiv.org/abs/2109.00692 |