Definition:Localization of Ring at Prime Ideal

Definition
Let $A$ be a commutative ring with unity.

Let $\mathfrak p$ be a prime ideal of $A$.

The localization of $A$ at $\mathfrak p$ is the localization of $A$ at the complement $A \setminus \mathfrak p$:
 * $A_{\mathfrak p} = \paren {A \setminus \mathfrak p}^{-1}A$

Also see

 * Complement of Prime Ideal of Ring is Multiplicatively Closed
 * Localization at Prime Ideal is Local Ring