It occurred to me that the rationals Q have also a unique prime factorization, as long as you allow negative exponents on the factorization.(adsbygoogle = window.adsbygoogle || []).push({});

If a/b is a rational, then both a and b have a unique (integer) prime factorization, and the fraction can be expressed uniquely as a product of primes, raised to the difference of the exponents found in the respective prime factors of a and b. Note that a/b does not even need to be reduced for this to work.

I find this a beautiful idea, but I ignore how to use it further, or what else can be constructed using it.

Edit: oops, except for zero... bye-bye to groups, rings, fields...

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# Prime factorization of rationals

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