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Ideals in the ring Q[X]

  1. Apr 6, 2006 #1
    Consider the ideal [tex]I[/tex] of [tex]Q[x][/tex] generated by the two polynomials [tex]f = x^2+1[/tex] and [tex]g=x^6+x^3+x+1[/tex]

    a) find [tex]h[/tex] in [tex]Q[x][/tex] such that [tex]I=<h>[/tex]
    b) find two polynomials [tex]s, t[/tex] in [tex]Q[x][/tex] such that [tex]h=sf+tg[/tex]
  2. jcsd
  3. Apr 6, 2006 #2
    Have you even given this problem a shot? It's fairly easy.
    Consider the ideal I of Z generated by 12 and 20. Do you know how to find a single number x that generates I? If you can't do this, you won't be able to do this problem either.
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