Rational function on an algebraic variety
= Rational function on an algebraic variety
{title2=$k(X)$}
= Rational functions on an algebraic variety
{synonym}
On an integral algebraic variety, a rational function is an equivalence class of regular functions on nonempty open subsets, with equality on a common dense open subset. These form the function field $k(X)$. On an affine open $\operatorname{Spec}A$, this field is the fraction field of $A$.
// Target: geometry-and-topology.bigb