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How can I prove that $\mathbb{Z}/p^q$, where $p$ is prime, is a UFD?

Well, I know that if $q=1$, it is because then it is a field.

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    If $q\neq 1$ then this is false, as the ring is not even an integral domain.2012-10-22
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    why it isn't an Integral Domain?2012-10-22
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    Please think a bit longer on this. Finding zero-divisors in the given ring is a good exercise that will really help you understand that ring.2012-10-22
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    okay, I understand. Thanks2012-10-22
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    @TobiasKildetoft Please consider converting your comment into an answer, so that this question gets removed from the [unanswered tab](http://meta.math.stackexchange.com/q/3138). If you do so, it is helpful to post it to [this chat room](http://chat.stackexchange.com/rooms/9141) to make people aware of it (and attract some upvotes). For further reading upon the issue of too many unanswered questions, see [here](http://meta.stackexchange.com/q/143113), [here](http://meta.math.stackexchange.com/q/1148) or [here](http://meta.math.stackexchange.com/a/9868).2013-06-20

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