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Topic: Can a small degree polynomial exist in this Ideal?
Replies: 6   Last Post: May 15, 2013 5:54 AM

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Robin Chapman

Posts: 40
Registered: 10/29/12
Re: Can a small degree polynomial exist in this Ideal?
Posted: May 14, 2013 6:37 AM
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On 14/05/2013 09:38, eric.fennessey@gmail.com wrote:
> I am feeling dim and my brain is failing me on this one.
>
> Let n,m >=2 and consider the subset, I, of polynomials in Z[X,Y]
> given by,
>
> I = {P.(X^n - 1) + Q.(Y^m - 1): P,Q in Z[X,Y]},
>
> I.e. the ideal generated by X^n -1, Y^m -1 in Z[X,Y].
>
> Let S be the subset of Z[X,Y] consisting of polynomials where each
> non-zero term of the form n.X^i.Y^j has i<n and j<m.
>
> My question is: Is I intersected with S the zero polynomial?


Yes.





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