Definition:Zariski Topology on Maximal Spectrum of Ring

Definition

Let $A$ be a commutative ring with unity.

Let $\map {\operatorname {MaxSpec} } A$ be its maximal spectrum.

Definition 1

The Zariski topology on $\map {\operatorname {MaxSpec} } A$ is the topology with as closed sets the maximal zero loci.

Definition 2

The Zariski topology on $\map {\operatorname{MaxSpec} } A$ is the subspace topology induced by the Zariski topology on the spectrum $\Spec A$.