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单词 StufeOfAField
释义

stufe of a field


The stufe of a field F is the least number n such that -1 can be expressed as a sum of n squares:

-1=a12++an2,

where each aiF. If no such an n exists, then we say that the stufe of F is .

Remarks.

  • The word “stufe”, meaning “level” in German, is attributed to mathematician Albrecht Pfister.

  • A theorem of Pfister asserts that in a field F, if -1 can be expressed as a finite sum of squares, then the stufe of F is a power of 2.

References

  • 1 A. Pfister, Zur Darstellung definiter Funktionen als Summe von Quadraten, Inventiones Mathematicae (1967).
  • 2 A. R. Rajwade, Squares, Cambridge University Press (1993).
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更新时间:2025/5/4 5:41:03