I'm sorry for unclear description of the problem.
So once again, let R = C[x_1,\dots,x_n]$ be my basering.
I'm looking for the group G, wich leaves a finite set S of polynomes
invariant under its action. So the ideal I = <S> is invariant under the
G-action too. And because every constant polynome is invariant under the
action, I can look at the subring C[I] = C[S] \subset R instead of
looking at I.
But of course you're right, there's a big difference between a ring and
an ideal.

greatz Johannes
Am 15.08.2011 21:10, schrieb Maarten Derickx:
> Dear Johannes,
> 
> I have a lot of trouble understanding your question. Your I is sometimes an 
> ideal and sometimes a ring and for me there is a huge difference between 
> those concepts (i.e. my rings always have an identity, and for every ring I 
> only one ideal with identity).
> 
> Thanks,
> Maarten
> 

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