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If F is a field than does it imply it must also be a Euclidean domain?

  1. Jun 6, 2007 #1
    1. The problem statement, all variables and given/known data
    If F is a field than does it imply it must also be a Euclidean domain?


    3. The attempt at a solution
    Yes since for any a,b in F. a=bq for some q in R. In fact let q=(b^-1)a. So the remainder which occurs in a ED is always 0. So the rule for being a ED is satisfied in any field.
     
    Last edited: Jun 6, 2007
  2. jcsd
  3. Jun 6, 2007 #2

    matt grime

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    Your answer starts with a minor error: a=1 and b=0 for instance contradict it.
     
  4. Jun 6, 2007 #3
    I should have added for any a,b not equal to 0.
     
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