Homological properties and finiteness of reducing invariants
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866918445705068544 |
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| author | Araya, Tokuji Hiramatsu, Naoya Takahashi, Ryo |
| author_facet | Araya, Tokuji Hiramatsu, Naoya Takahashi, Ryo |
| contents | We study reducing invariants of modules related to certain homological properties. For modules of finite reducing projective dimension, we establish grade inequalities. We prove that if $\mathbb{P}$ is the (uniform) Auslander condition, or the generalized Auslander--Reiten conjecture, or dependence of the total reflexivity conditions, then a module satisfies $\mathbb{P}$ provided that it has finite reducing invariant with respect to $\mathbb{P}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_12205 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Homological properties and finiteness of reducing invariants Araya, Tokuji Hiramatsu, Naoya Takahashi, Ryo Commutative Algebra 13C60, 13D05, 13D07 We study reducing invariants of modules related to certain homological properties. For modules of finite reducing projective dimension, we establish grade inequalities. We prove that if $\mathbb{P}$ is the (uniform) Auslander condition, or the generalized Auslander--Reiten conjecture, or dependence of the total reflexivity conditions, then a module satisfies $\mathbb{P}$ provided that it has finite reducing invariant with respect to $\mathbb{P}$. |
| title | Homological properties and finiteness of reducing invariants |
| topic | Commutative Algebra 13C60, 13D05, 13D07 |
| url | https://arxiv.org/abs/2604.12205 |