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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/2411.17581 |
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| _version_ | 1866915035944583168 |
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| author | Argudin-Monroy, Alejandro Bravo, Daniel Parra, Carlos E. |
| author_facet | Argudin-Monroy, Alejandro Bravo, Daniel Parra, Carlos E. |
| contents | We study the conditions under which a TTF class in a module category over a ring is silting. Using the correspondence between idempotent ideals over a ring and TTF classes in the module category, we focus on finding the necessary and sufficient conditions for $R/I$ to be a silting $R$-module, and hence for the TTF class $\mathbf{Gen}(R/I)$ to be silting, where $I$ is an idempotent two-sided ideal of $R$. In our main result, we show that $R/I$ is a silting module whenever $I$ is the trace of a projective $R$-module. Furthermore, we demonstrate that the converse holds for a broad class of rings, including semiperfect rings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_17581 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | TTF classes generated by silting modules Argudin-Monroy, Alejandro Bravo, Daniel Parra, Carlos E. Rings and Algebras 18e40, 16d90, 16S90, 16E30 We study the conditions under which a TTF class in a module category over a ring is silting. Using the correspondence between idempotent ideals over a ring and TTF classes in the module category, we focus on finding the necessary and sufficient conditions for $R/I$ to be a silting $R$-module, and hence for the TTF class $\mathbf{Gen}(R/I)$ to be silting, where $I$ is an idempotent two-sided ideal of $R$. In our main result, we show that $R/I$ is a silting module whenever $I$ is the trace of a projective $R$-module. Furthermore, we demonstrate that the converse holds for a broad class of rings, including semiperfect rings. |
| title | TTF classes generated by silting modules |
| topic | Rings and Algebras 18e40, 16d90, 16S90, 16E30 |
| url | https://arxiv.org/abs/2411.17581 |