Timeline for Analog to the Chinese Remainder Theorem in groups other than Z_n.
Current License: CC BY-SA 2.5
10 events
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| Jun 22, 2022 at 8:13 | history | edited | CommunityBot |
replaced http://math.uga.edu/~pete with http://alpha.math.uga.edu/~pete
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| Mar 21, 2010 at 23:10 | comment | added | darij grinberg | Ok, posted it as a new question: mathoverflow.net/questions/18959/… | |
| Mar 21, 2010 at 21:00 | comment | added | darij grinberg | Okay, I guess the module version follows from the ring-only version by applying the latter to the ring $R\oplus A$ (where multiplication inside $R\oplus 0$ is inherited from $R$, multiplication between $R\oplus 0$ and $0\oplus A$ is given by the $R$-module structure on $A$, and multiplication inside $0\oplus A$ is defined as identically zero), but this is quite artificial. I am wondering whether there is a simpler approach. | |
| Mar 21, 2010 at 20:57 | comment | added | darij grinberg | I am wondering: does the module version of the CRT (Under the same conditions as the ideal-theoretic CRT in the above post, if $A$ is an $R$-module, then the natural homomorphism $A/I_1\cdots I_nA = A/I_1A\cap\cdots \cap I_nA\to \bigoplus_{i=1}^{n} A/I_iA$ is an isomorphism of $R$-modules) directly follow from the above ring-only version (which is its particular case when $R=A$)? Because if not, I think it is the "real" generalization of the CRT, and the ring-only version should be considered a particular case. At least, I have used the module version more often than the ring-only one. | |
| Mar 21, 2010 at 16:41 | vote | accept | Ross Snider | ||
| Mar 21, 2010 at 3:27 | comment | added | Harry Gindi | +1 for the last part, which was interesting (and not on Wikipedia). | |
| Mar 21, 2010 at 2:41 | comment | added | Pete L. Clark | Thanks, Tom. You or anyone else can certainly feel free to correct typos in my answers if you feel like it -- I would view it as your doing me a favor. | |
| Mar 21, 2010 at 2:40 | history | edited | Pete L. Clark | CC BY-SA 2.5 |
edited body
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| Mar 21, 2010 at 2:38 | comment | added | Tom Leinster | Pete, there's a typo at the end of the first sentence of the statement of the Theorem. | |
| Mar 21, 2010 at 2:34 | history | answered | Pete L. Clark | CC BY-SA 2.5 |