Timeline for Factorizing polynomials in $\mathbf{Z}[[x]]$
Current License: CC BY-SA 2.5
12 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 26, 2011 at 11:44 | vote | accept | Tommaso Centeleghe | ||
| Feb 25, 2011 at 1:39 | answer | added | François Brunault | timeline score: 4 | |
| Feb 24, 2011 at 19:58 | answer | added | David E Speyer | timeline score: 2 | |
| Feb 24, 2011 at 12:09 | comment | added | François Brunault | @Tommaso : my feeling is that the equality you mention seems plausible. What you're asking seems to be a generalization of the isomorphism $\mathbf{Z}[[X]]/(X-p) \cong \mathbf{Z}_p$, but I don't see the proof in general... | |
| Feb 24, 2011 at 10:56 | comment | added | Tommaso Centeleghe | Nice, what are your feelings about the question then? Thanks. | |
| Feb 24, 2011 at 10:14 | comment | added | François Brunault | The ideal $\ker \varphi_{\alpha,\nu}$ is indeed principal. The proof is as follows : $\mathbf{Z}[[X]]$ is a Noetherian unique factorization domain, so every prime ideal of height $1$ is principal. But $\mathbf{Z}[[X]]$ has Krull dimension $2$ and the image of $\varphi_{\alpha,\nu}$ is not a field, so $\ker \varphi_{\alpha,\nu}$ is principal. | |
| Feb 22, 2011 at 19:43 | answer | added | Pace Nielsen | timeline score: 3 | |
| Feb 22, 2011 at 14:59 | history | edited | Tommaso Centeleghe | CC BY-SA 2.5 |
added 18 characters in body
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| Feb 22, 2011 at 14:54 | history | edited | Tommaso Centeleghe | CC BY-SA 2.5 |
added 158 characters in body
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| Feb 22, 2011 at 12:29 | comment | added | François Brunault | Maybe you could define $\varphi_{\alpha,\nu}$ on $\mathbf{Z}_p[[X]]$ instead ? Then you could try to use the Weierstrass preparation theorem. I don't know though if $\ker \varphi_{\alpha,\nu}$ is principal in your setting. | |
| Feb 22, 2011 at 11:53 | answer | added | Laurent Moret-Bailly | timeline score: 3 | |
| Feb 22, 2011 at 9:42 | history | asked | Tommaso Centeleghe | CC BY-SA 2.5 |