
Re: Can a small degree polynomial exist in this Ideal?
Posted:
May 14, 2013 6:37 AM


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 > nonzero 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.

