Gorenstein flat-cotorsion modules over tensor rings
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866916050708201472 |
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| author | Qin, Yongyun Yin, Chaobin |
| author_facet | Qin, Yongyun Yin, Chaobin |
| contents | Let $T_R(M)$ be a tensor ring, where $R$ is a ring and $M$ is an $N$-nilpotent $R$-bimodule. Under certain conditions, we characterize the Gorenstein flat-cotorsion modules over $T_R(M)$, showing that a $T_R(M)$-module $(X, u)$ is Gorenstein flat-cotorsion if and only if $u$ is monomorphic and $\Coker u$ is a Gorenstein flat-cotorsion $R$-module. As applications, we describe the Gorenstein flat-cotorsion modules over some trivial extension rings and Morita context rings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_27267 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Gorenstein flat-cotorsion modules over tensor rings Qin, Yongyun Yin, Chaobin Representation Theory Rings and Algebras Let $T_R(M)$ be a tensor ring, where $R$ is a ring and $M$ is an $N$-nilpotent $R$-bimodule. Under certain conditions, we characterize the Gorenstein flat-cotorsion modules over $T_R(M)$, showing that a $T_R(M)$-module $(X, u)$ is Gorenstein flat-cotorsion if and only if $u$ is monomorphic and $\Coker u$ is a Gorenstein flat-cotorsion $R$-module. As applications, we describe the Gorenstein flat-cotorsion modules over some trivial extension rings and Morita context rings. |
| title | Gorenstein flat-cotorsion modules over tensor rings |
| topic | Representation Theory Rings and Algebras |
| url | https://arxiv.org/abs/2605.27267 |