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An example of a non Noetherian UFD

How can I prove that $K[x_1, \ldots]$, with $K$ a field, is a UFD? That means there's a unique factorization. But how to prove it?


marked as duplicate by anon, Clayton, JSchlather, Zev Chonoles Jan 21 '13 at 19:11

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  • $\begingroup$ infinite, I know it is not noetherian but not why it is UFD $\endgroup$ – denere Jan 21 '13 at 18:48
  • $\begingroup$ Can you prove that $K[x_1,\ldots,x_n]$ is a UFD? Every element lives in such a subring, and you can use arguments about the degree of other variables to prove that the factorization in this ring is the only factorization in the larger ring. $\endgroup$ – Brett Frankel Jan 21 '13 at 18:50
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    $\begingroup$ Was the answer you received here not sufficient? $\endgroup$ – Zev Chonoles Jan 21 '13 at 18:51
  • $\begingroup$ you are rigth sorry, i didn't saw that $\endgroup$ – denere Jan 21 '13 at 18:52