Definition:Zariski Topology on Maximal Spectrum of Ring

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

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

Definition 1
The Zariski topology on $\operatorname{MaxSpec}(A)$ is the topology with as closed sets the maximal zero loci.

Definition 2
The Zariski topology on $\operatorname{MaxSpec}(A)$ is the subspace topology induced by the Zariski topology on the spectrum $\operatorname{Spec} A$.

Also see

 * Definition:Zariski Topology on Affine Algebraic Set