Integral domain
Field of fractions
Given an integral domain , the field of fractions is the smallest field into which it can be embedded. ring
Let .
Then for any and ,
then with
-
\begin{align*}
\frac{n}{d} = \frac{m}{b} \iff nb = md
\end{align*}
-
\begin{align*}
\frac{n}{d} \cdot \frac{m}{b} = \frac{nm}{db}
\end{align*}
\begin{align*}
\iota_{D} : D &\hookrightarrow \Frac D \
n &\mapsto \frac{ns}{s}
\end{align*}