Timeline for are intersections of kernels also kernels?
Current License: CC BY-SA 3.0
6 events
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| Sep 25, 2012 at 18:10 | comment | added | Qiaochu Yuan | @J. Martel: if you want to ask a question which only involves one vector space rather than two, you should probably ask it as a new question (and also clarify the relationship to your motivation, which I still don't really understand). | |
| Sep 25, 2012 at 18:09 | comment | added | Qiaochu Yuan | @J. Martel: it doesn't rule out that possibility. I explicitly use functoriality with respect to $V$ and $W$ separately. | |
| Sep 25, 2012 at 15:02 | comment | added | JHM |
I don't understand how you're argument could rule out the following possibility: suppose $V=W$ has finite dimension. Then $End(V)$ is a ring. Why could we not expect that there exists a polynomial $R$ in two variables over $End(V)$ with the following mystical' powers: given any two endomorphisms $S,T$ of $V$ the polynomial $R(S,T)$ has kernel exactly equal to the intersections of the kernels of $S,T$, or equal to the sum of the kernels of $S,T$? Does your argument really annihalate this possibility? I would think that the yield $R(S,T)$ should qualify as canonical'.
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| Sep 23, 2012 at 23:16 | comment | added | Qiaochu Yuan | This doesn't directly address the motivational question, but I admit that I don't really understand the relationship between the asked question and the motivational question. Doesn't the motivational question involve thinking about sums of kernels, not intersections? | |
| Sep 23, 2012 at 21:58 | history | edited | Qiaochu Yuan | CC BY-SA 3.0 |
added 87 characters in body; deleted 49 characters in body
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| Sep 23, 2012 at 21:52 | history | answered | Qiaochu Yuan | CC BY-SA 3.0 |