Contravariantly infinite resolving subcategories
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866912954536951808 |
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| author | Tanigawa, Gen |
| author_facet | Tanigawa, Gen |
| contents | Let $R$ be a commutative Noetherian ring. Denote by $\textrm{mod}R$ the category of finitely generated $R$-modules. In this paper, a contravariantly infinite subcategory of $\textrm{mod}R$ is defined as a full subcategory $\mathscr{X}$ of $\textrm{mod}R$ such that no module outside $\mathscr{X}$ admits a right $\mathscr{X}$-approximation. This paper provides several criteria for contravariant infiniteness in the case where $R$ is a local complete intersection. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_07945 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Contravariantly infinite resolving subcategories Tanigawa, Gen Commutative Algebra Representation Theory Let $R$ be a commutative Noetherian ring. Denote by $\textrm{mod}R$ the category of finitely generated $R$-modules. In this paper, a contravariantly infinite subcategory of $\textrm{mod}R$ is defined as a full subcategory $\mathscr{X}$ of $\textrm{mod}R$ such that no module outside $\mathscr{X}$ admits a right $\mathscr{X}$-approximation. This paper provides several criteria for contravariant infiniteness in the case where $R$ is a local complete intersection. |
| title | Contravariantly infinite resolving subcategories |
| topic | Commutative Algebra Representation Theory |
| url | https://arxiv.org/abs/2603.07945 |