\begin{definition}[Definition:Localization of Ring at Prime Ideal]
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 $A\setminus\mathfrak p$:
:$A_{\mathfrak p} = (A\setminus\mathfrak p)^{-1}A$
\end{definition}