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Euchlidean Domain

  1. Jan 16, 2006 #1
    I know this is a physics forum but I've got a quick question about a Euchlidean domain:

    Assuming that [itex] 1 - \sqrt {-7} [/itex]and [itex]2[/itex] are irreduclible, explain why[itex] Z[-7] [/itex] is not a euchlidean domain?

    This is a pure maths question and I've asked questions about other pure maths courses and got decent answers.

  2. jcsd
  3. Jan 16, 2006 #2
    There is no h in Euclidean.

    If Z[-7] were Euclidean, then in particular all irreducible elements would be prime. This leads to a contradiction.
  4. Jan 16, 2006 #3

    matt grime

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    Try multiplying 1-sqrt(-7) by its complex conjugate too.
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