The stable rank of $\mathbb{Z}[x]$ is $3$
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arXiv
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866910819161210880 |
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| author | Guyot, Luc |
| author_facet | Guyot, Luc |
| contents | Grunewald, Mennicke and Vaserstein proved that the Bass stable rank of $\mathbb{Z}[x]$, the ring of the univariate polynomials over $\mathbb{Z}$, is $3$. This note addresses minor errors found in their proof. Using their method, we show in addition that the unimodular row $(3, x + 1, x^2 + 16)$ is not stable. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2111_02965 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | The stable rank of $\mathbb{Z}[x]$ is $3$ Guyot, Luc Commutative Algebra 13D15 (Primary), 13B25 (Secondary) Grunewald, Mennicke and Vaserstein proved that the Bass stable rank of $\mathbb{Z}[x]$, the ring of the univariate polynomials over $\mathbb{Z}$, is $3$. This note addresses minor errors found in their proof. Using their method, we show in addition that the unimodular row $(3, x + 1, x^2 + 16)$ is not stable. |
| title | The stable rank of $\mathbb{Z}[x]$ is $3$ |
| topic | Commutative Algebra 13D15 (Primary), 13B25 (Secondary) |
| url | https://arxiv.org/abs/2111.02965 |