We compute the Witt ring kernel for an arbitrary field extension of degree 4 and characteristic different from 2 in terms of the coefficients of a polynomial determining the extension. In the case where the lower field is not formally real we prove that the intersection of any power n of its fundamental ideal and the Witt ring kernel is generated by n-fold Pfister forms. Let F be a field of characteristic different from 2. As usual denote by W (F ) the Witt ring of F , i.e. the ring of… CONTINUE READING