Definition:Vanishing Ideal of Set of Prime Ideals
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Definition
Let $A$ be a commutative ring with unity.
Let $V \subseteq \Spec A$ be a set of prime ideals of $A$.
Its vanishing ideal is its intersection, the set of elements of $A$ that are in each $\mathfrak p \in V$:
- $\map I V = \bigcap V$