Homework Help: Abstract algebra , intersection of ideals

1. Nov 24, 2011

okoolo

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?