If $R$ is a ring and $x$ is an indeterminate, what does the notation $R(x)$ mean? I've seen $R[x]$ but not $R(x)$.
1 Answer
$R(x)$ usually means the field of rational functions over $R$, i.e $\{\frac{f}{g}: f \in R[x], 0 \neq g \in R[x]\}$. (Alternatively, you can view this as the field of fractions of $R[x]$).