1. Limited time only! Sign up for a free 30min personal 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!

Ring and cosest

  1. Apr 2, 2012 #1
    I'm trying to list the cosets of the following ring and describe the relations that hold between these cosets.
    I'm using the division algorithm since x^2+1 is monic in the ring Z_4[x].Now for every f that belongs to Z_4[x] by the division algorithm
    f=(x^2+1)q(x)+p(x)=>the cosets are of the the form...a*x+b+I where I is an ideal generated by x^2+1.
    x^2+1=0 in the quotient=>a new ring where multiplication between cosets A+I and B+I is is defined by (A+I)(B+I)=(AB)+1 where the relation x^2+1=0 exists
    Is is ok?
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted

Similar Discussions: Ring and cosest
  1. Factor ring of a ring (Replies: 3)

  2. Ring theory? (Replies: 14)

  3. Boolean Ring (Replies: 3)