Timeline for Lifting identities of formal power series
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
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| Sep 2, 2012 at 16:50 | vote | accept | Dune | ||
| Aug 31, 2012 at 23:42 | comment | added | Qiaochu Yuan | In normed rings I think everything works out, and otherwise I'm not willing to speculate. It seems to me that without a norm you do not get very much control over what a convergent series looks like. | |
| Aug 31, 2012 at 22:37 | answer | added | Julian Rosen | timeline score: 5 | |
| Aug 31, 2012 at 20:05 | history | edited | Dune | CC BY-SA 3.0 |
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| Aug 31, 2012 at 19:51 | comment | added | Dune | Hi Will. You are talking about the universal property of formal power series, also mentioned at Wikipedia. This is indeed the solution for lifting those identities into certain rings with an I-adic topology, but unfortunately it does not generalize the theory of real or complex power series. I forgot mentioning that I am looking for such a generalization. | |
| Aug 31, 2012 at 19:26 | comment | added | Will Sawin | I can't think of any algebraic structure you would use here other than a topological ring. One case where this identity always holds is the completion of a local ring, where a power series that's not a polynomial converges only when $r$ lies in the maximal ideal, which allows one to truncate the power series when working in $R/m^n$ and then take the inverse limit. | |
| Aug 31, 2012 at 19:22 | history | edited | Dune |
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| Aug 31, 2012 at 19:16 | history | edited | Dune |
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| Aug 31, 2012 at 18:43 | history | asked | Dune | CC BY-SA 3.0 |