Abstract algebra , intersection of ideals

  • Thread starter okoolo
  • Start date
  • #1
1
0

Homework Statement



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


Homework Equations





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
 

Answers and Replies

Related Threads on Abstract algebra , intersection of ideals

Replies
1
Views
1K
  • Last Post
Replies
3
Views
2K
Replies
5
Views
3K
Replies
1
Views
2K
  • Last Post
Replies
0
Views
910
  • Last Post
Replies
3
Views
6K
Replies
4
Views
2K
Replies
2
Views
2K
Replies
4
Views
1K
Top