Timeline for What are the units of $\mathbb{Z}/4\mathbb{Z}[x]$?
Current License: CC BY-SA 2.5
5 events
| when toggle format | what | by | license | comment | |
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| Mar 25, 2011 at 10:18 | comment | added | Joshua P. Swanson | Thank you! The result you quoted jogged my memory. It's also problem 7.3.33(a) of Dummit and Foote (3rd Ed.). Part (b) gives the related result that $p(x) \in R[x]$ is nilpotent if and only if each coefficient is nilpotent (which was much easier to show). | |
| Mar 24, 2011 at 21:42 | comment | added | Ralph | The statement from Atiyah-Macdonald even holds for every graded ring $A = \bigoplus_{n \ge 0}A_n$ with unit: $a=(a_n)_{n \ge 0} \in A$ is a unit iff $a_0$ is a unit and $a_n$ is nilpotent for $n > 0$. | |
| Mar 24, 2011 at 10:26 | comment | added | Zev Chonoles | Ah, thanks for the correction Martin. | |
| Mar 24, 2011 at 10:22 | history | edited | Martin Brandenburg | CC BY-SA 2.5 |
added 11 characters in body
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| Mar 24, 2011 at 9:06 | history | answered | Zev Chonoles | CC BY-SA 2.5 |