(projectively coresolved) Gorenstein flat modules over tensor rings
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866908662466871296 |
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| author | Tang, Guoliang Wei, Jiaqun |
| author_facet | Tang, Guoliang Wei, Jiaqun |
| 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 projectively coresolved Gorenstein flat modules over $T_R(M)$, showing that a $T_R(M)$ module $(X,u)$ is projectively coresolved Gorenstein flat if and only if $u$ is monomorphic and $coker(u)$ is a projectively coresolved Gorenstein flat $R$-module. A class of Gorenstein at modules over $T_R(M)$ are also explicitly described. We discuss applications to trivial ring extensions and Morita context rings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_14494 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | (projectively coresolved) Gorenstein flat modules over tensor rings Tang, Guoliang Wei, Jiaqun Rings and Algebras Commutative Algebra 18G25, 16D90 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 projectively coresolved Gorenstein flat modules over $T_R(M)$, showing that a $T_R(M)$ module $(X,u)$ is projectively coresolved Gorenstein flat if and only if $u$ is monomorphic and $coker(u)$ is a projectively coresolved Gorenstein flat $R$-module. A class of Gorenstein at modules over $T_R(M)$ are also explicitly described. We discuss applications to trivial ring extensions and Morita context rings. |
| title | (projectively coresolved) Gorenstein flat modules over tensor rings |
| topic | Rings and Algebras Commutative Algebra 18G25, 16D90 |
| url | https://arxiv.org/abs/2511.14494 |