Construction of Gorenstein projective modules over tensor rings
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908610091548672 |
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| author | Zhao, Guoqiang Sun, Juxiang |
| author_facet | Zhao, Guoqiang Sun, Juxiang |
| contents | For a tensor ring $T_R(M)$, we obtain sufficient and necessary conditions to describe all complete projective resolutions and all Gorenstein projective modules. As a consequence, we provide a method for constructing Gorenstein projective modules over $T_R(M)$ from the ones of $R$. Some applications to trivial ring extensions, Morita context rings and triangular matrix rings are given. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_21454 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Construction of Gorenstein projective modules over tensor rings Zhao, Guoqiang Sun, Juxiang Commutative Algebra Representation Theory 16E05, 16E30, 16D90 For a tensor ring $T_R(M)$, we obtain sufficient and necessary conditions to describe all complete projective resolutions and all Gorenstein projective modules. As a consequence, we provide a method for constructing Gorenstein projective modules over $T_R(M)$ from the ones of $R$. Some applications to trivial ring extensions, Morita context rings and triangular matrix rings are given. |
| title | Construction of Gorenstein projective modules over tensor rings |
| topic | Commutative Algebra Representation Theory 16E05, 16E30, 16D90 |
| url | https://arxiv.org/abs/2510.21454 |