An algorithm for computing syzygies on $V[X]$ when $V$ is a valuation domain
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866914747909144576 |
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| author | Lombardi, Henri Quitté, Claude Yengui, Ihsen |
| author_facet | Lombardi, Henri Quitté, Claude Yengui, Ihsen |
| contents | We give an algorithm for computing the V-saturation of any finitely-generated submodule of a power of V[X], where V is a valuation domain. Our algorithm is based on a notion of "echelon form" which ensures its correctness. This allows us to compute a finite system of generators for the syzygy module of any finitely generated submodule of a power of V[X]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_00303 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | An algorithm for computing syzygies on $V[X]$ when $V$ is a valuation domain Lombardi, Henri Quitté, Claude Yengui, Ihsen Commutative Algebra 13CXX, 13PXX We give an algorithm for computing the V-saturation of any finitely-generated submodule of a power of V[X], where V is a valuation domain. Our algorithm is based on a notion of "echelon form" which ensures its correctness. This allows us to compute a finite system of generators for the syzygy module of any finitely generated submodule of a power of V[X]. |
| title | An algorithm for computing syzygies on $V[X]$ when $V$ is a valuation domain |
| topic | Commutative Algebra 13CXX, 13PXX |
| url | https://arxiv.org/abs/2304.00303 |