* Adam P. Goucher <apgoucher@gmx.com> [Feb 12. 2015 14:08]:
I suppose this question is subjective, but I would personally define 'a divides b' as:
`the ideal <b> is a subset of the ideal <a>'
in which case 0|0, but 0 doesn't divide any other integer. This seems to agree with the general intuition on this discussion thread, and also generalises to arbitrary integral domains.
In the context of GCD one sets GCD(a,0) = a. Now the GCD is the intersection of the multi-sets of exponents in the canonical prime factorization, so 0 has to be 0 = prod(k>=1, prime(k)^\infty ). This gives the same conclusion. Running off infinitely fast, jj
I'm afraid to post this question to MathOverflow, lest I be reprimanded for asking such an inappropriate question
THIS QUESTION DOES NOT APPEAR TO BE ABOUT RESEARCH LEVEL MATHEMATICS WITHIN THE SCOPE DEFINED IN THE HELP CENTER!!!
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