Syzygies of the residue field over Golod rings
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arXiv
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| Main Authors: | , , , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866908297730195456 |
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| author | Cuong, Doan Trung Dao, Hailong Eisenbud, David Kobayashi, Toshinori Polini, Claudia Ulrich, Bernd |
| author_facet | Cuong, Doan Trung Dao, Hailong Eisenbud, David Kobayashi, Toshinori Polini, Claudia Ulrich, Bernd |
| contents | Let $(R,m,k)$ be a Golod ring. We show a recurrent formula for high syzygies of $k$ interms of previous ones. In the case of embedding dimension at most $2$, we provided complete descriptions of all indecomposable summands of all syzygies of $k$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_13425 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Syzygies of the residue field over Golod rings Cuong, Doan Trung Dao, Hailong Eisenbud, David Kobayashi, Toshinori Polini, Claudia Ulrich, Bernd Commutative Algebra 13C13, 13D09, 13H10 Let $(R,m,k)$ be a Golod ring. We show a recurrent formula for high syzygies of $k$ interms of previous ones. In the case of embedding dimension at most $2$, we provided complete descriptions of all indecomposable summands of all syzygies of $k$. |
| title | Syzygies of the residue field over Golod rings |
| topic | Commutative Algebra 13C13, 13D09, 13H10 |
| url | https://arxiv.org/abs/2408.13425 |