Let k be an infinite field and let $X = {P_1, cdots, P_s}$ be a set of s-distinct points in $P^n$. We denote by $I(X)$ the defining ideal of $X$ in the polynomial ring $R = k[x_0, cdots, x_n]$ and by A the homogeneous coordinate ring of $X, A = sum_{t = 0}^{infty} A_t$.