Let V be a projective algebraic set defined as the set of the common zeros of a homogeneous ideal I in a polynomial ring R=K[x_0, x_1, \ldots, x_n] over a field K, and let A=R/I be the graded algebra of the polynomials over V.
All the definitions of the previous section apply, with the change that, when A or I appear explicitly in the definition, the value of the dimension must be reduced by one.