Gorenstein homological modules over tensor rings
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914193311006720 |
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| author | Di, Zhenxing Liang, Li Song, Zhiqian Tang, Guoliang |
| author_facet | Di, Zhenxing Liang, Li Song, Zhiqian Tang, Guoliang |
| contents | For a tensor ring $T_R(M)$, under certain conditions, we characterize the Gorenstein projective modules over $T_R(M)$, and prove that a $T_R(M)$-module $(X,u)$ is Gorenstein projective if and only if $u$ is monomorphic and ${\rm coker}(u)$ is a Gorenstein projective $R$-module. Gorenstein injective (resp., flat) modules over $T_R(M)$ are also explicitly described. Moreover, we give a characterization for the coherence of $T_R(M)$. Some applications to trivial ring extensions and Morita context rings are given. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_21349 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Gorenstein homological modules over tensor rings Di, Zhenxing Liang, Li Song, Zhiqian Tang, Guoliang Rings and Algebras K-Theory and Homology For a tensor ring $T_R(M)$, under certain conditions, we characterize the Gorenstein projective modules over $T_R(M)$, and prove that a $T_R(M)$-module $(X,u)$ is Gorenstein projective if and only if $u$ is monomorphic and ${\rm coker}(u)$ is a Gorenstein projective $R$-module. Gorenstein injective (resp., flat) modules over $T_R(M)$ are also explicitly described. Moreover, we give a characterization for the coherence of $T_R(M)$. Some applications to trivial ring extensions and Morita context rings are given. |
| title | Gorenstein homological modules over tensor rings |
| topic | Rings and Algebras K-Theory and Homology |
| url | https://arxiv.org/abs/2504.21349 |