Gorensteinness from duality pairs induced via Foxby equivalences
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912786620088320 |
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| author | Becerril, Víctor Pérez, Marco A. |
| author_facet | Becerril, Víctor Pérez, Marco A. |
| contents | We define and study induced duality pairs under Foxby equivalences. Given a semidualizing $(S,R)$-bimodule ${}_S C_R$, if $(\mathcal{A}_C(R),\mathcal{B}_C(R^{\rm op}))$ and $(\mathcal{A}_C(S^{\rm op}),\mathcal{B}_C(S))$ denote the duality pairs formed by the corresponding classes of Auslander and Bass modules, and if $(\mathcal{M,N})$ is a duality pair over $R$, we study the duality pair formed by the essential images of the restricted Foxby equivalences $(C \otimes_R \sim)|_{\mathcal{A}_C(R) \cap \mathcal{M}}$ and $\mathrm{Hom}_{R^{\rm op}}(C,\sim) |_{\mathcal{B}_C(R^{\rm op}) \cap \mathcal{N}}$, denoted by $\mathcal{M}^C(S)$ and $\mathcal{N}^C(S^{\rm op})$. We investigate which additional properties of the duality pair $(\mathcal{M,N})$ are transferred to $(\mathcal{M}^C(S),\mathcal{N}^C(S^{\rm op}))$. We also study several versions of Gorenstein injective and Gorenstein flat modules relative to the pairs $(\mathcal{A}_C(R) \cap \mathcal{M},\mathcal{B}_C(R^{\rm op}) \cap \mathcal{N})$ and $(\mathcal{M}^C(S),\mathcal{N}^C(S^{\rm op}))$. For instance, we explore the relation between these classes of modules under Foxby equivalences and under Pontryagin duality. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_20764 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Gorensteinness from duality pairs induced via Foxby equivalences Becerril, Víctor Pérez, Marco A. Rings and Algebras Category Theory 18G25, 18G10, 18G20, 16E10 We define and study induced duality pairs under Foxby equivalences. Given a semidualizing $(S,R)$-bimodule ${}_S C_R$, if $(\mathcal{A}_C(R),\mathcal{B}_C(R^{\rm op}))$ and $(\mathcal{A}_C(S^{\rm op}),\mathcal{B}_C(S))$ denote the duality pairs formed by the corresponding classes of Auslander and Bass modules, and if $(\mathcal{M,N})$ is a duality pair over $R$, we study the duality pair formed by the essential images of the restricted Foxby equivalences $(C \otimes_R \sim)|_{\mathcal{A}_C(R) \cap \mathcal{M}}$ and $\mathrm{Hom}_{R^{\rm op}}(C,\sim) |_{\mathcal{B}_C(R^{\rm op}) \cap \mathcal{N}}$, denoted by $\mathcal{M}^C(S)$ and $\mathcal{N}^C(S^{\rm op})$. We investigate which additional properties of the duality pair $(\mathcal{M,N})$ are transferred to $(\mathcal{M}^C(S),\mathcal{N}^C(S^{\rm op}))$. We also study several versions of Gorenstein injective and Gorenstein flat modules relative to the pairs $(\mathcal{A}_C(R) \cap \mathcal{M},\mathcal{B}_C(R^{\rm op}) \cap \mathcal{N})$ and $(\mathcal{M}^C(S),\mathcal{N}^C(S^{\rm op}))$. For instance, we explore the relation between these classes of modules under Foxby equivalences and under Pontryagin duality. |
| title | Gorensteinness from duality pairs induced via Foxby equivalences |
| topic | Rings and Algebras Category Theory 18G25, 18G10, 18G20, 16E10 |
| url | https://arxiv.org/abs/2512.20764 |