Vol. 63, No. 2, 1976

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Quadratic forms over nonformally real fields with a finite number of quaternion algebras

Craig McCormack Cordes

Vol. 63 (1976), No. 2, 357–365

This paper is concerned with quadratic forms over a nonformally real field, F, of characteristic not two, which has only a finite number, m, of quaternion algebras. The number q = |2| is always assumed to be finite. Of central importance will be the radical, R, which can be defined by R = {a G(1,)a = } where = F −{0} and G(1,a) is the set of nonzero elements represented by the form x2 ay2 over F. The main result here is that a finite Witt ring (and hence the complete quadratic form structure) is determined when m = 2 by the Witt group and the order of ∕R.

Mathematical Subject Classification
Primary: 10C05, 10C05
Received: 23 October 1975
Revised: 18 February 1976
Published: 1 April 1976
Craig McCormack Cordes