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Math Help - UFD Questions

  1. #1
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    UFD Questions

    Hello all,

    I have to questions regarding UFD's.

    1. Assume that Q[Sqrt(d)] is a UFD and that a is an integer in Q[Sqrt(d)] where a and a (with a bar above it) have no common factor, but the norm of a , N[ a] is a perfect square in Z. Can someone show that a is a perfect square in the quadratic integers in Q[Sqrt(d)] ?

    2. How can we prove that Z is a UFD?

    Thank you all, I appreciate the help!
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  2. #2
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    Quote Originally Posted by Samson View Post
    Hello all,

    I have to questions regarding UFD's.

    1. Assume that Q[Sqrt(d)] is a UFD and that a is an integer in Q[Sqrt(d)] where a and a (with a bar above it) have no common factor, but the norm of a , N[ a] is a perfect square in Z. Can someone show that a is a perfect square in the quadratic integers in Q[Sqrt(d)] ?

    2. How can we prove that Z is a UFD?

    Thank you all, I appreciate the help!
    I'm sure that there must be a generic prove to show that Z is a UFD. Here is what I have found thus far:
    http://people.ucsc.edu/~smohare/UFD.pdf

    Can someone turn that into Lehman's terms? Also, I still could use some help understanding part 1 as well.
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