Timeline for Descending chain of translation invariant linear spaces of polynomials
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
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| Jul 26, 2011 at 10:12 | comment | added | Torsten Ekedahl | A more highbrow explanation: $k[x_1,\ldots,x_n]$ is, as module over the constant-coefficient DO's, the injective hull of $k$ and as such is Artinian because the ring is Noetherian as is $k$ as module (the proof of this general fact is essentially by the argument Tom gives). | |
| Jul 26, 2011 at 10:06 | history | edited | Tom Goodwillie | CC BY-SA 3.0 |
added 12 characters in body
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| Jul 26, 2011 at 10:06 | comment | added | Tom Goodwillie | I meant "homogeneous ideal". I have edited accordingly. | |
| Jul 26, 2011 at 7:00 | comment | added | user16456 | What is a graded ideal? | |
| Jul 16, 2011 at 13:04 | comment | added | Tom Goodwillie | If $T_1$ properly contains $T_2$ then for some $D$ there is a degree $d$ polynomial in $T_1$ but not $T_2$. Then there is an element of degree $d$ in $D$ that annihilates one but not the other. | |
| Jul 16, 2011 at 11:31 | comment | added | user16456 | "An infinite descending chain $T_{\alpha}$ would give an infinite ascending chain $I(T_{\alpha})$..." This is true only if $T_1\ne T_2$ implies that the closure of $T_1$ is different from the closure of $T_2$.If $T_1$ and $T_2$ have the same closure, then $I(T_1)$ and $I(T_2)$ are the same. | |
| Jul 16, 2011 at 10:08 | history | answered | Tom Goodwillie | CC BY-SA 3.0 |