Timeline for Analog to the Chinese Remainder Theorem in groups other than Z_n.
Current License: CC BY-SA 2.5
6 events
| when toggle format | what | by | license | comment | |
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| Sep 8, 2018 at 23:09 | comment | added | arsmath | I think the proper generalization is described in this answer on Math Stack Exchange. | |
| Jan 7, 2018 at 9:24 | comment | added | Tri | There is the paper, "Polynomial Interpolation and the Chinese Remainder Theorem for Algebraic Systems," Mathematische Zeitschrift 143 (1975), pp. 165-174, by Baker and Pixley. | |
| Mar 21, 2010 at 4:53 | comment | added | Peter Arndt | Hm, now that I think about it I agree - the main statement of the CRT for rings is probably that the ideals being coprime implies that the product map is surjective. The rest is the general nonsense I exposed above. I don't know of any application of this, nor of any other part of Universal Algebra, other than not having to think again about such things for each new algebraic structure. I appreciated to see the scope of validity of these principles, though. | |
| Mar 21, 2010 at 4:27 | comment | added | Pete L. Clark | Is this truly a generalization of the ring-theoretic CRT? It seems to say only that the CRT homomorphism is injective, which is the obvious part of the theorem. The meat of it is to prove the surjectivity. Also, does this universal algebra result have "mainstream" applications? | |
| Mar 21, 2010 at 4:26 | history | edited | Peter Arndt | CC BY-SA 2.5 |
added 61 characters in body
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| Mar 21, 2010 at 4:14 | history | answered | Peter Arndt | CC BY-SA 2.5 |