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Find a number that is algebraic with degree 3 over Z_3

  1. Feb 15, 2008 #1
    1. The problem statement, all variables and given/known data
    I want to find a number that is algebraic with degree 3 over Z_3. To do this, I need to find an extension field of Z_3. Q,R, and Z_p (p greater than 3) definitely will not work because they have different algebra. Anyone?


    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Feb 15, 2008 #2

    Hurkyl

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    How about the algebraic closure of Z_3? Or is that too nonconstructuve?

    Well, at least we know that no matter what extension field E you use and number [itex]\alpha[/itex] you select, there has to be a map [itex]\pi : (\mathbb{Z} / 3\mathbb{Z})[t] \to E[/itex] with [itex]\pi(t) = \alpha[/itex].
     
    Last edited: Feb 15, 2008
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