In the context of commutative algebra, a Jacobson ring is a ring that satisfies certain properties related to its prime ideals and maximal ideals. Specifically, a ring \( R \) is called a **Jacobson ring** if the intersection of all maximal ideals of \( R \) is equal to the nilradical of \( R \).
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A commutative ring is Jacobson when every prime ideal is the intersection of the maximal ideals containing it. Equivalently, for every ideal , its radical is the intersection of the maximal ideals containing .