 For showing the relationship between the degree of a projective algebraic set and the Hilbert series, consider an projective algebraic set , defined as the set of the zeros of a homogeneous ideal formula_44, where is a field, and let formula_45 be the ring of the regular functions on the algebraic set.In this section, one does not need irreducibility of algebraic sets nor primality of ideals.Also, as Hilbert series are not changed by extending the field of coefficients, the field is supposed, without loss of generality, to be algebraically closed.