nLab
rational function

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

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