Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Polynomial Rings

  1. Jan 23, 2012 #1


    User Avatar
    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


    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?

  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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook