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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2409.08393 |
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| _version_ | 1866910861909557248 |
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| author | Gillespie, James Iacob, Alina |
| author_facet | Gillespie, James Iacob, Alina |
| contents | We show that Iacob-Iyengar's answer to a question of Avromov-Foxby extends from Noetherian to coherent rings. In particular, a coherent ring R is regular if and only if the injective (resp. projective) dimension of each complex X of R-modules agrees with its graded-injective (resp. graded-projective) dimension. The same is shown for the analogous dimensions based on FP-injective R-modules, and on flat R-modules. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_08393 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Homological dimensions of complexes over coherent regular rings Gillespie, James Iacob, Alina Commutative Algebra 16E65, 18G25, 18N40 We show that Iacob-Iyengar's answer to a question of Avromov-Foxby extends from Noetherian to coherent rings. In particular, a coherent ring R is regular if and only if the injective (resp. projective) dimension of each complex X of R-modules agrees with its graded-injective (resp. graded-projective) dimension. The same is shown for the analogous dimensions based on FP-injective R-modules, and on flat R-modules. |
| title | Homological dimensions of complexes over coherent regular rings |
| topic | Commutative Algebra 16E65, 18G25, 18N40 |
| url | https://arxiv.org/abs/2409.08393 |