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!

When do quadratic polynomials generate the same ideal?

  1. Apr 24, 2017 #1
    1. The problem statement, all variables and given/known data
    When do two quadratic polynomials in ##\mathbb{Z}_3 [x]## generate the same ideal?

    2. Relevant equations


    3. The attempt at a solution
    I feel like they generate the same ideal only when they have the same coefficients, but am not sure how to show this.
     
  2. jcsd
  3. Apr 26, 2017 #2

    fresh_42

    Staff: Mentor

    It's not necessary for your question, as you only asked about principal ideals. Nevertheless, is ##\mathbb{Z}_3[x]## a principle ideal domain?
    Now to approach your question. As always, write down what is given, namely two ideals ##I=\langle p(x) \rangle## and ##J=\langle q(x)\rangle## with polynomials ##p(x),q(x)\in \mathbb{Z}_3[x]## and ##I=J##. The latter means ##p(x) \in J## and ##q(x) \in I##. What can you conclude from this?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: When do quadratic polynomials generate the same ideal?
  1. Polynomials and Ideals (Replies: 13)

Loading...