Dg-separable dg-extensions
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866912803181297664 |
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| author | Zimmermann, Alexander |
| author_facet | Zimmermann, Alexander |
| contents | We define and characterise completely dg-separable dg-extensions $φ:(A,d_A)\rightarrow (B,d_B)$. We completely characterise the case of graded commutative dg-division algebras in characteristic different from $2$. We prove that for a dg-separable extension a short exact sequence of dg-modules over $(B,d_B)$ splits if and only if the restriction to $(A,d_A)$ splits. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_06526 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Dg-separable dg-extensions Zimmermann, Alexander Rings and Algebras Representation Theory Primary: 16E45, Secondary: 12H05, 13A02, 16W50 We define and characterise completely dg-separable dg-extensions $φ:(A,d_A)\rightarrow (B,d_B)$. We completely characterise the case of graded commutative dg-division algebras in characteristic different from $2$. We prove that for a dg-separable extension a short exact sequence of dg-modules over $(B,d_B)$ splits if and only if the restriction to $(A,d_A)$ splits. |
| title | Dg-separable dg-extensions |
| topic | Rings and Algebras Representation Theory Primary: 16E45, Secondary: 12H05, 13A02, 16W50 |
| url | https://arxiv.org/abs/2412.06526 |