On quadratic forms over inseparable quadratic extensions
Copyright policy )On quadratic forms over inseparable quadratic extensions
The author discusses quadratic forms under inseparable quadratic extensions \(K=k (\sqrt{d})\), where \(\text{char } k=2\). He proves the following theorem that is sharper than that conjectured by \textit{R. Baeza} [Math. Z. 135, 175-184 (1974; Zbl 0263.15015)], namely, if \(q\) is a non- singular anisotropic \(k\)-form of dimension \(4m\) or \(4m+2\) with the Witt index over \(K\) greater than \(m\), then it has a subform \(q'\perp dq'\) for some non-singular \(k\)-form \(q'\) of dimension two.
- Louisiana State University United States
Algebraic field extensions, non-singular anisotropic form, inseparable quadratic extensions, Algebraic theory of quadratic forms; Witt groups and rings, Quadratic and bilinear forms, inner products, Quadratic forms over general fields, quadratic forms
Algebraic field extensions, non-singular anisotropic form, inseparable quadratic extensions, Algebraic theory of quadratic forms; Witt groups and rings, Quadratic and bilinear forms, inner products, Quadratic forms over general fields, quadratic forms
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