stufe of a field
The stufe of a field is the least number such that can be expressed as a sum of squares:
where each . If no such an exists, then we say that the stufe of is .
Remarks.
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The word “stufe”, meaning “level” in German, is attributed to mathematician Albrecht Pfister.
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A theorem of Pfister asserts that in a field , if can be expressed as a finite sum of squares, then the stufe of is a power of .
References
- 1 A. Pfister, Zur Darstellung definiter Funktionen als Summe von Quadraten, Inventiones Mathematicae (1967).
- 2 A. R. Rajwade, Squares, Cambridge University Press (1993).