Timeline for Do there exist general conditions for cyclicity of unit groups of quotient rings (generalizations of the primitive root theorem)?
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| May 15, 2020 at 4:56 | comment | added | Pete L. Clark | Thanks, that's helpful. | |
| May 14, 2020 at 16:46 | comment | added | R. van Dobben de Bruyn | For your final question: as in my proof, it is necessary that $\mathfrak m/\mathfrak m^2$ has dimension $0$ or $1$ over $R/\mathfrak m$. Such rings are always principal; see e.g. Prop. 8.8 in Atiyah–MacDonald. (In fact, using the Cohen structure theorem plus a little computation, any finite local Artinian ring with $\dim \mathfrak m/\mathfrak m^2 = 1$ can be written as a quotient of a finite extension of $\mathbf Z_p$ ― this was my first approach until I realised it's really a question about Artinian rings.) | |
| May 14, 2020 at 13:00 | comment | added | Daniel Santiago | Wow thank you so much!! I had been told the classification results that I asked for along the lines of Gilmer's work exist but I had trouble finding them. It is amazing to see old results be rediscovered like this. | |
| May 14, 2020 at 11:19 | history | edited | Pete L. Clark | CC BY-SA 4.0 |
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| May 14, 2020 at 9:35 | history | answered | Pete L. Clark | CC BY-SA 4.0 |