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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2406.06078 |
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| _version_ | 1866915857995661312 |
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| author | Kuroki, Ryota |
| author_facet | Kuroki, Ryota |
| contents | We give a constructive proof of the general Nullstellensatz: a univariate polynomial ring over a commutative Jacobson ring is Jacobson. This theorem implies that every finitely generated algebra over a zero-dimensional ring or the ring of integers is Jacobson, which has been an open problem in constructive algebra. We also prove a variant of the general Nullstellensatz for finitely Jacobson rings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_06078 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A constructive proof of the general Nullstellensatz for Jacobson rings Kuroki, Ryota Commutative Algebra 13F20 (Primary) 03F65 (Secondary) We give a constructive proof of the general Nullstellensatz: a univariate polynomial ring over a commutative Jacobson ring is Jacobson. This theorem implies that every finitely generated algebra over a zero-dimensional ring or the ring of integers is Jacobson, which has been an open problem in constructive algebra. We also prove a variant of the general Nullstellensatz for finitely Jacobson rings. |
| title | A constructive proof of the general Nullstellensatz for Jacobson rings |
| topic | Commutative Algebra 13F20 (Primary) 03F65 (Secondary) |
| url | https://arxiv.org/abs/2406.06078 |