Timeline for Relation(s) between units and nilpotent elements in graded noncommutative rings
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
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| Jan 19, 2023 at 22:29 | answer | added | Dmitri Piontkovski | timeline score: 1 | |
| Dec 16, 2022 at 16:14 | comment | added | M.G. | @PaceNielsen: Thanks for the reply! I basically copied the lemma from the BCW's paper. If I understand you correctly, you are saying that the non-trivial direction of the equivalence in the lemma also holds for non-homogeneous elements $r$ as long as all the components are of positive degree? | |
| Dec 16, 2022 at 16:08 | comment | added | Pace Nielsen | In your lemma you don't need $r$ to have positive degree. Rather, you need the grade-$0$ component of $r$ to be zero. For question 2, you might look at some of the work Agata Smoktunowicz did on graded nil rings. Really weird things can happen. | |
| Dec 16, 2022 at 15:37 | history | edited | M.G. | CC BY-SA 4.0 |
edited title
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| Dec 16, 2022 at 12:55 | history | edited | M.G. | CC BY-SA 4.0 |
clarified characteristic 0
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| Dec 16, 2022 at 12:50 | history | edited | M.G. | CC BY-SA 4.0 |
clarified characteristic 0
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| Dec 16, 2022 at 12:48 | comment | added | M.G. | @abx: My apologies, I implicitly meant characteristic 0. I will fix that immediately. | |
| Dec 16, 2022 at 9:23 | comment | added | R. van Dobben de Bruyn | However, you can easily fix (1) either by replacing $f'$ by $f-f(0)$, or by making it a one-sided implication "$\Rightarrow$" like in (2). | |
| Dec 16, 2022 at 7:34 | comment | added | abx | Your "standard facts " are not correct. In $\mathbb{F}_p[x]$, $1+x^p$ satisfies the hypotheses of 1. but is not invertible, and $g(x)=x^p$ is not nilpotent though $g'(x)=0$. | |
| Dec 16, 2022 at 4:21 | history | asked | M.G. | CC BY-SA 4.0 |