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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2410.05888 |
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| _version_ | 1866910721731723264 |
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| author | Bennett-Tennenhaus, Raphael |
| author_facet | Bennett-Tennenhaus, Raphael |
| contents | We consider the category of linear relations over an arbitrary commutative ring, and identify it as a subcategory of the category of Kronecker representations. We observe that this subcategory forms a definable, faithful and hereditary torsion-free class. We also generalise results used in the functorial filtrations method, known before only in case the ground ring is a field. In particular, our results strictly generalise what the so-called the `covering' and `splitting' properties from this method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_05888 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Linear relations over commutative rings Bennett-Tennenhaus, Raphael Representation Theory Primary 16D70, Secondary 18E40 We consider the category of linear relations over an arbitrary commutative ring, and identify it as a subcategory of the category of Kronecker representations. We observe that this subcategory forms a definable, faithful and hereditary torsion-free class. We also generalise results used in the functorial filtrations method, known before only in case the ground ring is a field. In particular, our results strictly generalise what the so-called the `covering' and `splitting' properties from this method. |
| title | Linear relations over commutative rings |
| topic | Representation Theory Primary 16D70, Secondary 18E40 |
| url | https://arxiv.org/abs/2410.05888 |