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Abstract Algebra - ideals and generators

  1. Jan 26, 2012 #1
    1. The problem statement, all variables and given/known data
    a.) Let a=3-8i and b=2+3i. Find x,y ϵ Z[i] such that ax+by=1.
    b.) Show explicitly that the ideal I=(85,1+13i) [itex]\subseteq[/itex] Z[i] is principle by exhibiting a generator.
    2. Relevant equations
    Given ideal: I=(85,1+13i) [itex]\subseteq[/itex] Z[i]
    a=3-8i
    b=2+3i

    Honestly, I am beyond lost on this problem. Any help would be appreciated. Thanks!
     
  2. jcsd
  3. Jan 26, 2012 #2

    micromass

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    You should apply the division algorithm in a suitable way.
     
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