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A Note on Quadratic Forms and the u-invariant

Published online by Cambridge University Press:  20 November 2018

Roger Ware
Roger Ware*
Affiliation:
University of Kansas, Lawrence, Kansas; The Pennsylvania State University, University Park, Pennsylvania
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The u-invariant of a field F, u = u(F), is defined to be the maximum of the dimensions of anisotropic quadratic forms over F. If F is a non-formally real field with a finite number q of square classes then it is known that u ≦ q. The purpose of this note is to give some necessary and sufficient conditions for equality in terms of the structure of the Witt ring of F.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 26 , Issue 5 , October 1974 , pp. 1242 - 1244
Copyright
Copyright © Canadian Mathematical Society 1974

References

1. Brocker, L., Über eine Klasse pythagoreischer Körper, Arch. Math. 23 (1972), 405–407.Google Scholar
2. Diller, J. and Dress, A., Zür Galoistheorie pythagoreischer Körper, Arch. Math. 16 (1965), 148–152.Google Scholar
3. Elman, R. and Lam, T. Y., Quadratic forms over formally real and Pythagorean fields, Amer. J. Math. 94- (1972), 1155–1194.Google Scholar
4. Elman, R. and Lam, T. Y., Quadratic forms and the u-invariant, I, Math. Z. 131 (1973), 283–304.Google Scholar
5. Lorenz, F., Quadratische Formen uber Korpern, Springer Lecture Notes 130 (1970).Google Scholar
6. Ware, R., When are Witt rings group rings, Pacific J. Math. 49 (1973), 279–284.Google Scholar
7. Cordes, C., The Witt group and the equivalence of fields with respect to quadratic forms, J. Algebra 26 (1973), 400–421.Google Scholar