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> Jannick Asmus wrote:
>
> > On 21.10.2006 09:33, Sasha P wrote:
> >
> >> Consider ideal
> >> I={f \in C[0,1] : lim_{x \to 0} f(x)/x^n=0,
> n=0,1,2,â??}
> >> Is I prime ideal?
> >
> > At least I is radical, i.e. if f^n in I for some
> n>0, then f in I. This
> > is one step towards being a prime ideal.
>
> Is it true that f^n in I => f in I?
> What if f(x) = x * x^{n/2} ?
>
> --
> Timothy Murphy
> e-mail (<80k only): tim /at/ birdsnest.maths.tcd.ie
> tel: +353-86-2336090, +353-1-2842366
> s-mail: School of Mathematics, Trinity College,
> Dublin 2, Ireland
No, the limit must be equal to zero for any n=0,1,2,... For example
f(x)=exp(-1/x^2) \in I.
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