Category:Zariski Topology

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This category contains results about Zariski Topology.
Definitions specific to this category can be found in Definitions/Zariski Topology.


On an Affine Space

Let $k$ be a field.

Let $\mathbb A^n \left({k}\right) = k^n$ denote the standard affine space of dimension $n$ over $k$.


The Zariski topology on $\mathbb A^n \left({k}\right)$ is the topology on the direct product $k^n$ whose closed sets are the affine algebraic sets in $\mathbb A^n \left({k}\right)$.


On the spectrum of a ring

Let $A$ be a commutative ring with unity.

Let $\operatorname{Spec} \left({A}\right)$ be the prime spectrum of $A$.


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

Pages in category "Zariski Topology"

This category contains only the following page.