Timeline for How to classify the algebras C^∞(M)?
Current License: CC BY-SA 2.5
4 events
| when toggle format | what | by | license | comment | |
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| Apr 14, 2010 at 23:46 | comment | added | Martin Brandenburg | thanks michael and emerton. I've added some remarks in my original question. | |
| Apr 14, 2010 at 23:42 | history | edited | Martin Brandenburg | CC BY-SA 2.5 |
fixed latex
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| Apr 14, 2010 at 17:12 | comment | added | Emerton | Note also that, if $M$ is positive dimensional, then $C^{\infty}(M)$ is not Noetherian, since if $\mathfrak m$ is a maximal ideal corresponding to a point $x \in M$, then $\bigcap_{n \geq 0} \mathfrak m^n$ is non-zero (since there are non-zero smooth functions whose Taylor series is identically zero). This also rules out polynomial or power-series rings. | |
| Apr 14, 2010 at 15:04 | history | answered | Michael Bächtold | CC BY-SA 2.5 |