Finiteness criteria for Gorenstein homological dimension and some invariants of groups
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866929742962229248 |
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| author | Kaperonis, Ilias Stergiopoulou, Dimitra-Dionysia |
| author_facet | Kaperonis, Ilias Stergiopoulou, Dimitra-Dionysia |
| contents | In this paper, we study finiteness criteria for the Gorenstein homological dimension of groups over a commutative ring of finite Gorenstein weak global dimension and provide estimates for the Gorenstein weak global dimension of group rings. As a result, we obtain Gorenstein analogues of well known properties in classical homological algebra over large families of infinite groups. Moreover, we prove that over a commutative ring of finite Gorenstein weak global dimension, the Gorenstein cohomological dimension of a group G bounds its Gorenstein homological dimension. Finally, we compare the generalized cohomological dimension and the generalized homological dimension of a group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_02768 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Finiteness criteria for Gorenstein homological dimension and some invariants of groups Kaperonis, Ilias Stergiopoulou, Dimitra-Dionysia Commutative Algebra Rings and Algebras 18G20 In this paper, we study finiteness criteria for the Gorenstein homological dimension of groups over a commutative ring of finite Gorenstein weak global dimension and provide estimates for the Gorenstein weak global dimension of group rings. As a result, we obtain Gorenstein analogues of well known properties in classical homological algebra over large families of infinite groups. Moreover, we prove that over a commutative ring of finite Gorenstein weak global dimension, the Gorenstein cohomological dimension of a group G bounds its Gorenstein homological dimension. Finally, we compare the generalized cohomological dimension and the generalized homological dimension of a group. |
| title | Finiteness criteria for Gorenstein homological dimension and some invariants of groups |
| topic | Commutative Algebra Rings and Algebras 18G20 |
| url | https://arxiv.org/abs/2311.02768 |