# Give me your most general form of the chinese remainder theorem. [closed]

## closed as not a real question by Victor Protsak, Loop Space, Theo Johnson-Freyd, Bill Johnson, S. Carnahan♦Sep 10 '10 at 0:29

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-1: The title is obnoxious and the questioner didn't put even minimal effort into formulating the question. – Victor Protsak Sep 9 '10 at 19:38
Knew it reminded me of something. en.wikipedia.org/wiki/The_New_Colossus – Will Jagy Sep 9 '10 at 21:21

## 2 Answers

There is a chapter in the award-winning book The Mathematical Experience by Philip J. Davis and Reuben Hersh which can serve as an answer to this question. Its title is

"The Drive to Generality and Abstraction. The Chinese Remainder Theorem: A Case Study"

See (if you can)

http://books.google.com/books?id=lMdz84dWNnAC&pg=PA187&lpg=PA187&dq=Chinese+Remainder+Theorem+The+Mathematical+Experience&source=bl&ots=Bq8ZMmP8u3&sig=yd0hbM_VZR9TxzcFZWHth87obng&hl=en&ei=3i6JTM2uNorG8wTmnvHgDg&sa=X&oi=book_result&ct=result&resnum=3&ved=0CCUQ6AEwAg#v=onepage&q&f=false

It is an interesting take in part because Davis and Hersh are not algebraists or number theorists. Note that they do not include the result on pairwise comaximal ideals in a commutative ring, which is the most general result that I have in mind when I say "Chinese Remainder Theorem". On the other hand, they do discuss the interpretation of weak approximation as a sort of CRT. (In my view this is a good analogy but not precisely right: when both results apply, CRT has a stronger conclusion than weak approximation.)

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This MO question contains a nice version for groups and half a Chinese remainder theorem (at most) for general algebraic structures.

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