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Questions about modular forms and related areas
5
votes
Ideal in ring of power series
The answer is "no". Take $n=3$ and an arbitrary prime $p\ge3$. Let $\alpha=X_3^{p^3}+X_1X_2^{p^2-1}$ and $\beta=X_3^{p^3}+X_1^{p-1}X_2$. Both are irreducible elements, not belonging to $I$, but their …