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Feb 27, 2016 at 20:01 comment added KConrad I think the last paragraph here should have gone first: it is a very concrete illustration of something weird that can happen. In a Dedekind domain the property of being able to write every ratio of nonzero elements in its fraction field in "lowest terms" is in fact equivalent to it being a UFD.
Jun 1, 2010 at 5:29 history edited Pete L. Clark CC BY-SA 2.5
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Jun 1, 2010 at 5:13 history answered Pete L. Clark CC BY-SA 2.5