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Homework Help: 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.
    R=Z_4[x]/((x^2+1)*Z_4[x])
    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
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