Definition:Vanishing Set of Subset of Ring
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Definition
Let $A$ be a commutative ring with unity.
Let $S \subseteq A$ be a subset.
The vanishing set of $S$ is the set of prime ideals of $A$ containing $S$:
- $\map V S = \set {\mathfrak p \in \Spec A: \mathfrak p \supseteq S}$
Also known as
The vanishing set of $S$ is also known as the zero locus of $S$.