Symbolic power of a prime ideal

Definition

Let $R$ be a commutative unital ring, $Q$ a prime ideal of $R$ and $n$ a positive integer. The $n^{th}$ symbolic power of $Q$, denoted as $Q^{(n)}$ is defined as the set:

$\{r\in R|sr\in Q^{n},s\in R\setminus Q\}$

Equivalently, it is the pre-image of the $n^{th}$ power of the localized ideal $Q_{Q}$ in the localization $R_{Q}$.