Definition:Nilradical of Ring/Definition 2
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Definition
Let $A$ be a commutative ring with unity.
Let $\Spec A$ denote the prime spectrum of $A$.
The nilradical of $A$ is:
- $\ds \Nil A = \bigcap_{\mathfrak p \mathop \in \Spec A} \mathfrak p$
That is, it is the intersection of all prime ideals of $A$.