\begin{definition}[Definition:Localization of Ring at Element]
Let $A$ be a commutative ring with unity.
Let $f\in A$ be an element.
The '''localization of $A$ at $f$''' is the localization of $A$ at the set of powers $\{1, f, f^2, \ldots\}$:
:$A_f = (\{1, f, f^2, \ldots\})^{-1}A$
\end{definition}