Alexander Sivatski: The Witt ring kernel for a fourth degree field extension

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

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