1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    Dick

    User Avatar
    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?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook