Give me your most general form of the chinese remainder theorem. - MathOverflow [closed]most recent 30 from http://mathoverflow.net2013-05-19T16:35:38Zhttp://mathoverflow.net/feeds/question/38208http://www.creativecommons.org/licenses/by-nc/2.5/rdfhttp://mathoverflow.net/questions/38208/give-me-your-most-general-form-of-the-chinese-remainder-theoremGive me your most general form of the chinese remainder theorem.unknown (google)2010-09-09T17:45:51Z2010-09-09T19:11:03Z
<p>This one is related:
<a href="http://mathoverflow.net/questions/21782/generalized-chinese-remainder-theorem" rel="nofollow">http://mathoverflow.net/questions/21782/generalized-chinese-remainder-theorem</a></p>
http://mathoverflow.net/questions/38208/give-me-your-most-general-form-of-the-chinese-remainder-theorem/38209#38209Answer by Peter Arndt for Give me your most general form of the chinese remainder theorem.Peter Arndt2010-09-09T17:52:24Z2010-09-09T17:52:24Z<p><a href="http://mathoverflow.net/questions/18893/analog-to-the-chinese-remainder-theorem-in-groups-other-than-z-n" rel="nofollow">This</a> MO question contains a nice version for groups and half a Chinese remainder theorem (at most) for general algebraic structures.</p>
http://mathoverflow.net/questions/38208/give-me-your-most-general-form-of-the-chinese-remainder-theorem/38218#38218Answer by Pete L. Clark for Give me your most general form of the chinese remainder theorem.Pete L. Clark2010-09-09T19:11:03Z2010-09-09T19:11:03Z<p>There is a chapter in the award-winning book <em>The Mathematical Experience</em> by Philip J. Davis and Reuben Hersh which can serve as an answer to this question. Its title is</p>
<p>"The Drive to Generality and Abstraction. The Chinese Remainder Theorem: A Case Study"</p>
<p>See (if you can)</p>
<p><a href="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" rel="nofollow">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</a></p>
<p>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.) </p>