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 $\Spec A$ 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.