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In Surprising Generalizations, it is mentioned that Chinese remainder theorem and Lagrange interpolation are specific instances of the same thing, my question is what is their common generalisation/abstraction ?

Thank you

PS : Should there be a Generalisation tag ? to be used when one knows a specific concept and is looking for it's generalisation/more-abstract forms?

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    Did you read the wikipedia article http://en.wikipedia.org/wiki/Chinese_remainder_theorem#Statement_for_principal_ideal_domains? I think it answers your question (at any rate, it's the answer I would give). Namely, both the classical CRT and Lagrange interpolation are special cases of a CRT in more general ring $R$. The most direct generalization is when $R$ is a PID: in particular then one still has an "explicit solution". A more general generalization is to any finite set of comaximal ideals in any commutative ring.2011-07-28
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    You know, you could have clicked on the names in the question you link to... You would have landed [here (Harry's name)](http://mathoverflow.net/questions/10014/applications-of-the-chinese-remainder-theorem/10017#10017) and [here (Qiaochu's name)](http://www.artofproblemsolving.com/Forum/blog.php?b=10595) - the latter because Q. linked to that thread in a comment to Harry's answer, in case you wonder...2011-07-28
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    @Theo : I assumed the names link to profiles and not the content that was being referred to, That's why I didn't click them, I did wonder why someone would give refrences to people for helping with an intresting result but not the result itself. Funy enogh I looked at other posts/replies to see if anyone would mention the original post.2011-07-28
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    Yeah, it is well-hidden :) It took me a moment to figure that out.2011-07-28

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