rational function

Given a commutative ring $R$, the commutative ring of **rational functions** with coefficients in $R$ is the field of fractions of the polynomial ring $R[z]$.

Let $X$ be an affine variety over a field $k$ with the ring of regular function?s $\mathcal{O}(X)$. A **rational function** is any element of the field of fractions of $\mathcal{O}(X)$, that is the function field of the variety.

In either case, rational functions are equivalence classes of fractions; they need not be functions defined everywhere.

Revised on December 9, 2009 05:17:22
by Toby Bartels
(173.60.119.197)