Generalised Buchberger and Schreyer algorithms for strongly discrete coherent rings
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866915033322094592 |
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| author | Neuwirth, Stefan Lombardi, Henri Yengui, Ihsen |
| author_facet | Neuwirth, Stefan Lombardi, Henri Yengui, Ihsen |
| contents | Let M be a finitely generated submodule of a free module over a multivariate polynomial ring with coefficients in a discrete coherent ring. We prove that its module MLT(M ) of leading terms is countably generated and provide an algorithm for computing explicitly a generating set. This result is also useful when MLT(M ) is not finitely generated. Suppose that the base ring is strongly discrete coherent. We provide a Buchberger-like algorithm and prove that it converges if, and only if, the module of leading terms is finitely generated. We also provide a constructive version of Hilbert's syzygy theorem by following Schreyer's method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_16460 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Generalised Buchberger and Schreyer algorithms for strongly discrete coherent rings Neuwirth, Stefan Lombardi, Henri Yengui, Ihsen Commutative Algebra Let M be a finitely generated submodule of a free module over a multivariate polynomial ring with coefficients in a discrete coherent ring. We prove that its module MLT(M ) of leading terms is countably generated and provide an algorithm for computing explicitly a generating set. This result is also useful when MLT(M ) is not finitely generated. Suppose that the base ring is strongly discrete coherent. We provide a Buchberger-like algorithm and prove that it converges if, and only if, the module of leading terms is finitely generated. We also provide a constructive version of Hilbert's syzygy theorem by following Schreyer's method. |
| title | Generalised Buchberger and Schreyer algorithms for strongly discrete coherent rings |
| topic | Commutative Algebra |
| url | https://arxiv.org/abs/2411.16460 |