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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Accesso online: | https://arxiv.org/abs/2512.22132 |
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| _version_ | 1866915696107061248 |
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| author | Zhao, Guoqiang Sun, Juxiang |
| author_facet | Zhao, Guoqiang Sun, Juxiang |
| contents | Let $T_R(M)$ be a tensor ring and $\mathcal{X}$, $\mathcal{Y}$ be two classes of $R$-modules. Under certain conditions, we prove that a $T_R(M)$-module $(A, u)$ is $Ind(\mathcal{X})$-Gorenstein projective if and only if $u$ is monomorphic and $coker(u)$ is an $\mathcal{X}$-Gorenstein projective $R$-module. $\mathcal{Y}$-Gorenstein injective $T_R(M)$-modules are also explicitly described. As a consequence, the characterizations of Ding projective and Ding injective modules over $T_R(M)$ are obtained. Some applications to trivial ring extensions and Morita context rings are given. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_22132 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $\mathcal{X}$-Gorenstein projective and $\mathcal{Y}$-Gorenstein injective modules over tensor rings Zhao, Guoqiang Sun, Juxiang Rings and Algebras 18G25, 16D90 Let $T_R(M)$ be a tensor ring and $\mathcal{X}$, $\mathcal{Y}$ be two classes of $R$-modules. Under certain conditions, we prove that a $T_R(M)$-module $(A, u)$ is $Ind(\mathcal{X})$-Gorenstein projective if and only if $u$ is monomorphic and $coker(u)$ is an $\mathcal{X}$-Gorenstein projective $R$-module. $\mathcal{Y}$-Gorenstein injective $T_R(M)$-modules are also explicitly described. As a consequence, the characterizations of Ding projective and Ding injective modules over $T_R(M)$ are obtained. Some applications to trivial ring extensions and Morita context rings are given. |
| title | $\mathcal{X}$-Gorenstein projective and $\mathcal{Y}$-Gorenstein injective modules over tensor rings |
| topic | Rings and Algebras 18G25, 16D90 |
| url | https://arxiv.org/abs/2512.22132 |