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Homework Help: Polynomial Rings

  1. Jan 23, 2012 #1

    jgens

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    Gold Member

    1. The problem statement, all variables and given/known data

    Find eight elements [itex]r \in \mathbb{Q}[x]/(x^4-16)[/itex] such that [itex]r^2=r[/itex].

    2. Relevant equations

    N/A

    3. The attempt at a solution

    The elements [itex]0+(x^4-16)[/itex] and [itex]1+(x^4-16)[/itex] clearly satisfy the desired properties, but I still need six more elements. Can anyone help me figure out a technique for finding a few more elements?

    Thanks!
     
  2. jcsd
  3. Jan 23, 2012 #2
    You can always brute force it. An arbitrary element in your ring has the form [itex][ax^3+bx^2+cx+d][/itex]. Square it and see when the relation is satisfied.
     
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