1. A Note on Quadratic Forms and the u-invariant
- Author
-
Roger Ware
- Subjects
Pure mathematics ,General Mathematics ,010102 general mathematics ,u-invariant ,Isotropic quadratic form ,01 natural sciences ,Definite quadratic form ,Quadratic formula ,Discriminant ,Quadratic form ,Quartic function ,0103 physical sciences ,Binary quadratic form ,010307 mathematical physics ,0101 mathematics ,Mathematics - Abstract
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.
- Published
- 1974
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