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Homework Help: Algebraic over a field

  1. Mar 26, 2009 #1
    1. The problem statement, all variables and given/known data
    K is a field, F is an extension field of K.
    If u is algebraic over K, u an element of F, show u-1 is algebraic over K

    I'm trying to find a contradiction when I assume u-1 is transcendental, but I am not getting very far... anything to steer me in the right direction.
  2. jcsd
  3. Mar 26, 2009 #2


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    Science Advisor
    Homework Helper

    Don't try and do it by contradiction. If u is algebraic then it's a root of a polynomial over K. Try and find a polynomial that u^(-1) satisfies. Here's an example. If u satisfies x^2+2x+3, I'm pretty sure u^(-1) will satisfy 1+2x+3x^2. Why?
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