Definition 10.64.1. Let $R$ be a ring. Let $\mathfrak p$ be a prime ideal. For $n \geq 0$ the $n$th *symbolic power* of $\mathfrak p$ is the ideal $\mathfrak p^{(n)} = \mathop{\mathrm{Ker}}(R \to R_\mathfrak p/\mathfrak p^ nR_\mathfrak p)$.

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