تقرير
The stable rank of $\mathbb{Z}[x]$ is $3$
| العنوان: | The stable rank of $\mathbb{Z}[x]$ is $3$ |
|---|---|
| المؤلفون: | Guyot, Luc |
| سنة النشر: | 2021 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Commutative Algebra, 13D15 (Primary), 13B25 (Secondary) |
| الوصف: | 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. Comment: 9 pages, no figure. This new version integrates suggestions from Pace Nielsen, Alain Valette and Yves Cornulier. Proposition B displays now a simpler unstable unimodular row |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2111.02965 |
| رقم الأكسشن: | edsarx.2111.02965 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |