Système homogène de paramètres en codimension 1 et indépendance analytique

We provide an algorithm computing an h.s.o.p of the graded k-algebra k[X_]/〈F〉 where F is an homogeneous polynomial of degree >0 nonzero, with coefficients in an arbitrary field k. Then we generalize in some sense this algorithm to the case of an homogeneous polynomial of degree >0 and primitive with coefficients in an arbitrary commutative ring. This generalization allows us to control the number of radical generators of an ideal generated by a sequence annihilated by a homogeneous polynomial of degree >0 and primitive. We deduce the analytic independence property of a s.o.p. of a Noetherian local ring (thanks to the Krull's principal ideal theorem) and a characterization of the Krull dimension of a Noetherian ring like the characterization of the general Krull dimension given in [7].