Definition:Zariski Topology/Spectrum of Ring

Definition
Let $A$ be a commutative ring with unity.

Let $\Spec A$ be the prime spectrum of $A$.

The Zariski topology on $\operatorname{Spec} A$ is the topology with closed sets the vanishing sets $\map V S$ for $S \subseteq A$.

Also see

 * Vanishing Sets of Subsets of Ring Satisfy Closed Set Axioms
 * Definition:Zariski Topology on Maximal Spectrum of Ring