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It is easy to show that a PID must be noetherian. My question is:

Does UFD imply noetherian? If not, is there an easy counterexample?

I apologize if this turns out to be a simple question. Thanks in advance!

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    http://en.wikipedia.org/wiki/Unique_factorization_domain (see **Properties** and also **Equivalent conditions for a ring to be a UFD***2012-12-09

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