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  "body": "\n## Summary\n\nThe Jacobson topology, or hull-kernel topology, is a topology on the set $\\operatorname{Prim}(R)$ of [[primitive ideals|M0JDQR0V5S]] of a ring $R$.\nA set of primitive ideals is closed when it consists of all primitive ideals that contain some fixed ideal.\nFor a commutative ring it is the [[Zariski topology|8SQK7RTB63]] restricted to maximal ideals.\nSo the space $\\operatorname{Prim}(R)$ is a noncommutative analogue of the [[spectrum of a ring|FB45BHHA2J]].\nFor a commutative C*-algebra $C_0(X)$ it recovers the space $X$.\nFor this reason it is the standard topology on the primitive spectrum of a C*-algebra.\n\n## Explanations\n\n### L1 human\n\nFor a commutative ring the maximal ideals behave like points, and the Zariski topology turns them into a geometric space.\nIn a noncommutative ring the right replacement for points is the primitive ideals, the annihilators of simple modules.\nThe Jacobson topology declares a set of these points closed when it is \"cut out by an ideal\": it is all the points that contain that ideal.\nFor the integers the points are the ideals $p\\Z$, and the closed sets are the finite sets of primes together with the whole space.\n",
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