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Regenbogen
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François G. Dorais
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How to prove that the subrings of the ratinalrational numbers are noetherian?

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How to prove that the subrings of the ratinal numbers are noetherian?

I have managed to prove that the aforementioned subrings are in bijection with the subsets of the primes, however, I haven't been able to prove that they are all noetherian. I need help.