In [5], Cox introduced the homogeneous coordinate ring of a toric variety, which is a polynomial ring that allows to show that such a variety behaves like a projective space in many ways. An analogous to that ring can also be defined for a smooth projective variety X over an algebraically closed field k such that linear and numerical equivalence coincide for divisors on X, condition which is assumed for all varieties considered in this paper. Indeed, let us fix {[Li]} r i= 1 a Z-basis of Pic (X), and set n=(n1, n2,..., nr)∈ Zr and