Properties of quasi-projective dimension over abelian categories
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866912602691469312 |
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| author | Chen, Hongxing Chen, Xiaohu Liu, Mengge |
| author_facet | Chen, Hongxing Chen, Xiaohu Liu, Mengge |
| contents | Quasi-projective dimension was introduced by Gheibi, Jorgensen and Takahashi to generalize the Auslander-Buchsbaum formula and the depth formula in commutative algebra. In this paper, we establish some basic properties of quasi-projective dimensions of objects in abelian categories. Analogous to global dimension of rings, we also introduce the concept of quasi-global dimension for left Noetherian rings, and then compare quasi-global dimension with global dimension for a class of Nakayama algebras. This provides new examples of finite-dimensional algebras with finite quasi-global dimensions but infinite global dimensions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_20137 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Properties of quasi-projective dimension over abelian categories Chen, Hongxing Chen, Xiaohu Liu, Mengge Rings and Algebras Commutative Algebra Category Theory Quasi-projective dimension was introduced by Gheibi, Jorgensen and Takahashi to generalize the Auslander-Buchsbaum formula and the depth formula in commutative algebra. In this paper, we establish some basic properties of quasi-projective dimensions of objects in abelian categories. Analogous to global dimension of rings, we also introduce the concept of quasi-global dimension for left Noetherian rings, and then compare quasi-global dimension with global dimension for a class of Nakayama algebras. This provides new examples of finite-dimensional algebras with finite quasi-global dimensions but infinite global dimensions. |
| title | Properties of quasi-projective dimension over abelian categories |
| topic | Rings and Algebras Commutative Algebra Category Theory |
| url | https://arxiv.org/abs/2509.20137 |