A theorem on the values of quadratic forms over fields. (Q2551134)
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| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A theorem on the values of quadratic forms over fields. |
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A theorem on the values of quadratic forms over fields. (English)
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1971
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The following theorem is proved: Let \(q\) be an anisotropic quadratic form over an arbitrary field \(K\) and let \(E/K\) be an algebraic field extension of finite degree \(n\). Then for any \(c\) in \(E\) which is represented by \(q\) over \(E\), the norm \(N_{E/K}(c)\) is a product of \(n\) elements which are represented by \(q\) over \(K\). In a slightly weaker form this theorem had been conjectured by E. Witt (unpublished).
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