Category:Definitions/Zariski Topology

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This category contains definitions related to Zariski Topology.
Related results can be found in Category:Zariski Topology.

On an Affine Space

Let $k$ be a field.

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

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

On the spectrum of a ring

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 $S \subseteq A$.