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arXiv · 2111.02965

The stable rank of $\mathbb{Z}[x]$ is $3$

Luc Guyot
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Abstract

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.

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Luc Guyot. 2025-02-09. The stable rank of $\mathbb{Z}[x]$ is $3$. https://doi.org/10.1016/j.exmath.2025.125659

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