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Show that the ring of all rational numbers $m/n$ with $n$ an odd integer is a principal ideal domain.

We haven't really discussed principal ideal domains. I've heard that this is easy, but I just lack the basic knowledge of what a principal ideal domain is.

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    http://en.wikipedia.org/wiki/Principal_ideal_domain2012-05-02
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    Sorry, but... if you don't have the "basic knowledge of what a principal domain is", then how can you possibly expect a proof showing that something *is* a principal ideal domain to be "easy"? Even a basic reader would be hard if you try to read it in russian and you don't know the alphabet! I could tell you that this is easy because the ring in question is a localization of a PID, but that's unlikely to be "easy" or enlightening to you...2012-05-02
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    Related to http://math.stackexchange.com/questions/137876/a-subring-of-the-field-of-fractions-of-a-pid-is-a-pid-as-well2012-05-03

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