Submission: 2008, Mar 24
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.
2000 Mathematics Subject Classification: 15A63
Keywords and Phrases: Witt ring, quadratic form, Pfister form, polynomial
Full text: dvi.gz 14 k, dvi 29 k, ps.gz 652 k, pdf.gz 99 k, pdf 115 k.