Results 1 to 2 of 2

Math Help - ideal and quotient ring

  1. #1
    gkz
    gkz is offline
    Newbie
    Joined
    Feb 2010
    Posts
    1

    ideal and quotient ring

    hi, i'm having trouble doing this question. I'm not sure how to start it.
    Any help?

    Thanks
    Attached Thumbnails Attached Thumbnails ideal and quotient ring-123.bmp  
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member
    Joined
    Nov 2008
    Posts
    394
    Quote Originally Posted by gkz View Post
    hi, i'm having trouble doing this question. I'm not sure how to start it.
    Any help?

    Thanks
    Hint) Verify that I is an ideal, written <x^2 +1>. Since x^2 + 1 is irreducible in R=R[x] and R is PID, <x^2 +1> is a maximal ideal in R It follows that R[x]/<x^2+1> is a field. Let \alpha=x+<x^2+1>. Then, an elements of R[x]/<x^2+1> has the form k_1 + k_2\alpha, where k_1, k_2 \in R. I leave it to you to fill the remaining steps.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. ideal,nil,nilpotent ideal in prime ring
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: May 24th 2011, 07:57 AM
  2. Ideal of the ring
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: March 27th 2011, 09:15 PM
  3. Ideal of ring
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: December 16th 2009, 09:58 PM
  4. Ring without maximal ideal
    Posted in the Advanced Algebra Forum
    Replies: 8
    Last Post: December 6th 2009, 08:01 AM
  5. ring/ideal
    Posted in the Advanced Algebra Forum
    Replies: 5
    Last Post: November 19th 2009, 02:52 PM

Search Tags


/mathhelpforum @mathhelpforum