Timeline for Bass' stable range of $\mathbf Z[X]$
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
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| Feb 17, 2018 at 21:40 | comment | added | Luc Guyot | @Oblomov There is a flaw in the (very last part of) proof of Proposition 1.9 of Grunewald et al. Therefore $(21 + 4x, 12, x^2 + 20)$ is not guaranteed to be non-reducible (and I cannot show that it is reducible). I elaborate a little bit on this in my answer below. | |
| Feb 16, 2018 at 17:19 | history | edited | YCor | CC BY-SA 3.0 |
wrote a statement to clarify everything
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| S Sep 17, 2016 at 12:36 | history | suggested | Luc Guyot | CC BY-SA 3.0 |
Fixed typo related to brackets
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| Sep 17, 2016 at 12:25 | review | Suggested edits | |||
| S Sep 17, 2016 at 12:36 | |||||
| Oct 24, 2013 at 14:12 | comment | added | Oblomov | The answer is given in a paper of Grunewald, Mennicke and Vaserstein (On the groups $SL_2(\mathbf Z[x])$ and $SL_2(k[x,y])$). Israel J. Math. 86 (1994), no. 1-3, 157–193). One example of unimodular row that is not reducible is the following $(21+ 4x, 12, x^2 + 20)$. | |
| Oct 24, 2013 at 14:11 | vote | accept | Oblomov | ||
| Jun 18, 2013 at 13:00 | comment | added | Steven Landsburg | Wilberd: Right. I no longer understand why I thought this mattered. Thanks for making this clear. | |
| Jun 18, 2013 at 4:04 | comment | added | Wilberd van der Kallen | If the ideal $I$ is not principal, this makes no difference. Suppose $[\bar f,\bar g]$ is unimodular modulo $I$. Choose $p$, $q\in \Bbb Z[x]$ so that $h:=pf+qg-1\in I$. Then $(f,g,h)$ is a unimodular row that is not reducible. | |
| Jun 7, 2013 at 19:41 | history | answered | Steven Landsburg | CC BY-SA 3.0 |