Gorenstein categories and separable equivalences
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866918092442959872 |
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| author | Zhao, Guoqiang Sun, Juxiang |
| author_facet | Zhao, Guoqiang Sun, Juxiang |
| contents | Let $\mathscr{C}$ be an additive subcategory of left $Λ$-modules, we establish relations of the orthogonal classes of $\mathscr{C}$ and (co)res $\widetilde{\mathscr{C}}$ under separable equivalences. As applications, we obtain that the (one-sided) Gorenstein category and Wakamatsu tilting module are preserved under separable equivalences. Furthermore, we discuss when $G_{C}$-projective (injective) modules and Auslander (Bass) class with respect to $C$ are invariant under separable equivalences. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_23243 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Gorenstein categories and separable equivalences Zhao, Guoqiang Sun, Juxiang Representation Theory Commutative Algebra 16D20, 16E30, 16G10 Let $\mathscr{C}$ be an additive subcategory of left $Λ$-modules, we establish relations of the orthogonal classes of $\mathscr{C}$ and (co)res $\widetilde{\mathscr{C}}$ under separable equivalences. As applications, we obtain that the (one-sided) Gorenstein category and Wakamatsu tilting module are preserved under separable equivalences. Furthermore, we discuss when $G_{C}$-projective (injective) modules and Auslander (Bass) class with respect to $C$ are invariant under separable equivalences. |
| title | Gorenstein categories and separable equivalences |
| topic | Representation Theory Commutative Algebra 16D20, 16E30, 16G10 |
| url | https://arxiv.org/abs/2506.23243 |