# Definition:Zariski Topology/Spectrum of Ring

< Definition:Zariski Topology(Redirected from Definition:Zariski Topology on Prime Spectrum of Ring)

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## Definition

Let $A$ be a commutative ring with unity.

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

The **Zariski topology** on $\Spec A$ 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

- Results about
**Zariski topology**can be found**here**.

## Source of Name

This entry was named for Oscar Zariski.