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Polynomial factor rings

  1. Aug 23, 2008 #1
    Let A be the integers modulo 7.
    b(x)= x^3 -2 and c(x) = x^3 + 2 are polynomials in A[x].

    How can you show that A/<b(x)> and A/<c(x)> have the same number of elements? In this practice problem I already showed that A/<b(x)> and A/<c(x)> are fields by showing that <b(x)> and <c(x)> are maximal ideals, but I don't know how this helps.
  2. jcsd
  3. Aug 24, 2008 #2


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    you stated it wrong it seems. you want A[x]/<whatever>. then it gets easier.
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