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Math Help - Ring extension problem - is Z[sqrt(10)] a UFD?

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    Question Ring extension problem - is Z[sqrt(10)] a UFD?

    Hi,

    I am trying to determine whether Z[sqrt(10)] is a unique factorization domain (UFD), and can't seem to do it.
    I'd guess that it isn't, since 10 = sqrt(10) * sqrt(10) = 2*5 are seemingly two different factorizations of it, but how do I prove that 2,5 and sqrt(10) are irreducibles?

    Is there any better way to do it?
    Last edited by DanEshel; November 26th 2012 at 03:56 AM.
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