Ein Kriterium für die Richtigkeit der Milnor-Vermutung

Let F denote a field of characteristic ≠2. The Witt ring WF (i.e. the ring of similarity classes of quadratic forms with coefficients in F) will be characterized by taking the similarity classes of certain Pfister forms 2] as generators and using suitable relations among them (theorem 1). In order to characterize GF, the graded ring associated to WF, in terms of generators and relations Milnor 4] constructed a homomorphism from his ring k_*F onto GF and conjectured this homomorphism to be an isomorphism. This conjecture turns out to be equivalent to a problem on ideals in a commutative ring (theorem 2).