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:


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


  • 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.


  • 1 A. Pfister, Zur Darstellung definiter Funktionen als Summe von Quadraten, Inventiones Mathematicae (1967).
  • 2 A. R. Rajwade, Squares, Cambridge University Press (1993).
Title stufe of a field
Canonical name StufeOfAField
Date of creation 2013-03-22 15:06:01
Last modified on 2013-03-22 15:06:01
Owner CWoo (3771)
Last modified by CWoo (3771)
Numerical id 5
Author CWoo (3771)
Entry type Definition
Classification msc 15A63
Classification msc 12D15
Synonym level of a field
Related topic TheoremsOnSumsOfSquares
Defines stufe