Can someone give any hint on how to start? I have a feeling that I have to prove that all maximal ideals containing $I$ will contain the radical of $I$.
2026-03-30 13:41:26.1774878086
Prove that radical of an ideal is contained in the Jacobson of the ideal
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The radical of $I$ equals the intersection of the prime ideals containing $I$. Every maximal ideal is prime so the radical is contained in every maximal ideal containing $I$.