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Abstract algebra , intersection of ideals

  1. Nov 24, 2011 #1
    1. The problem statement, all variables and given/known data

    prove that <x^m> intersection <x^n> = <x^LCM(m,n)>


    2. Relevant equations



    3. The attempt at a solution

    ===>

    let b be in <x^n> intersection <x^m>

    then for some t,k,p in Z, b=x^(mt) = x^(nk) thus b=x^(LCM(m,n) * p i.e. b is in <x^LCM(m,n)>

    <===

    let b be in <x^LCM(m,n)>
    let s=lcm(m,n) =mt=nk for some t,k in Z

    then for some r in Z , b=x^(sr)

    then b = x^(mt)r =x^(nk)r

    and that's where I'm stuck..

    I was also considering trying to find and isomorphic mapping from one set to another..

    any ideas?
    thanks, Adam
     
  2. jcsd
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