Definition: Zariski Topology of a Commutative Ring

Let \(\operatorname{Spec}(R)\) be the sectrum of a commutative ring \(R\). We can make \(R\) a topological space, if we assert that for any subset \(T\subseteq R\) the set. \[D(T):=\left\{I\in \operatorname {Spec} \left(R\right){|}\,T\not \subseteq I\right\}\] is open. This topology is called the Zariski topology on \(R\) and is named after the mathematician Oscar Zariski.

Propositions: 1

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Adapted from CC BY-SA 3.0 Sources:

  1. Brenner, Prof. Dr. rer. nat., Holger: Various courses at the University of Osnabrück