Totally acyclic complexes and homological invariants over arbitrary rings
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866913146858373120 |
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| author | Wang, Jian Li, Yunxia Hu, Jiangsheng zhu, Haiyan |
| author_facet | Wang, Jian Li, Yunxia Hu, Jiangsheng zhu, Haiyan |
| contents | In this paper, we investigate equivalent characterizations of the condition that every acyclic complex of projective, injective, or flat modules is totally acyclic over a general ring R. We provide examples to illustrate relationships among these conditions and show that several are closely tied to the homological invariants silp(R), spli(R) and sfli(R). We also give sufficient conditions for the equality spli(R) = silp(R), thereby refining results due to Ballas-Chatzistavridis and Wang-Yang. Further, we extend a result of Christensen-Foxby-Holm on characterizations of Iwanaga-Gorenstein rings to the non-commutative setting. This generalizes a theorem of Estrada-Fu-Iacob, offering additional equivalent characterizations under a general assumption while also yielding characterizations of the Nakayama conjecture. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_23277 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Totally acyclic complexes and homological invariants over arbitrary rings Wang, Jian Li, Yunxia Hu, Jiangsheng zhu, Haiyan Rings and Algebras K-Theory and Homology In this paper, we investigate equivalent characterizations of the condition that every acyclic complex of projective, injective, or flat modules is totally acyclic over a general ring R. We provide examples to illustrate relationships among these conditions and show that several are closely tied to the homological invariants silp(R), spli(R) and sfli(R). We also give sufficient conditions for the equality spli(R) = silp(R), thereby refining results due to Ballas-Chatzistavridis and Wang-Yang. Further, we extend a result of Christensen-Foxby-Holm on characterizations of Iwanaga-Gorenstein rings to the non-commutative setting. This generalizes a theorem of Estrada-Fu-Iacob, offering additional equivalent characterizations under a general assumption while also yielding characterizations of the Nakayama conjecture. |
| title | Totally acyclic complexes and homological invariants over arbitrary rings |
| topic | Rings and Algebras K-Theory and Homology |
| url | https://arxiv.org/abs/2506.23277 |