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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2409.11892 |
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| _version_ | 1866912033646051328 |
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| author | Bao, Yanhong Lü, Jiafeng Zhao, Zhibing |
| author_facet | Bao, Yanhong Lü, Jiafeng Zhao, Zhibing |
| contents | Let $S/R$ be a Frobenius extension with $_RS_R$ centrally projective over $R$. We show that if $_Rω$ is a Wakamatsu tilting module then so is $_SS\otimes_Rω$, and the natural ring homomorphism from the endomorphism ring of $_Rω$ to the endomorphism ring of $_SS\otimes_Rω$ is a Frobenius extension in addition that pd$(ω_T)$ is finite, where $T$ is the endomorphism ring of $_Rω$. We also obtain that the relative $n$-torsionfreeness of modules is preserved under Frobenius extensions. Furthermore, we give an application, which shows that the generalized G-dimension with respect to a Wakamatsu module is invariant under Frobenius extensions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_11892 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Relative torsionfreeness and Frobenius extensions Bao, Yanhong Lü, Jiafeng Zhao, Zhibing Rings and Algebras 16D10, 16E05, 16E30 Let $S/R$ be a Frobenius extension with $_RS_R$ centrally projective over $R$. We show that if $_Rω$ is a Wakamatsu tilting module then so is $_SS\otimes_Rω$, and the natural ring homomorphism from the endomorphism ring of $_Rω$ to the endomorphism ring of $_SS\otimes_Rω$ is a Frobenius extension in addition that pd$(ω_T)$ is finite, where $T$ is the endomorphism ring of $_Rω$. We also obtain that the relative $n$-torsionfreeness of modules is preserved under Frobenius extensions. Furthermore, we give an application, which shows that the generalized G-dimension with respect to a Wakamatsu module is invariant under Frobenius extensions. |
| title | Relative torsionfreeness and Frobenius extensions |
| topic | Rings and Algebras 16D10, 16E05, 16E30 |
| url | https://arxiv.org/abs/2409.11892 |