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Homestufe of a field

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# 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:

$-1=a_{1}^{2}+\cdots+a_{n}^{2},$ |

where each $a_{i}\in F$. If no such an $n$ exists, then we say that the *stufe* of $F$ is $\infty$.

Remarks.

# References

- 1 A. Pfister, Zur Darstellung definiter Funktionen als Summe von Quadraten, Inventiones Mathematicae (1967).
- 2 A. R. Rajwade, Squares, Cambridge University Press (1993).

Defines:

stufe

Related:

TheoremsOnSumsOfSquares

Synonym:

level of a field

Type of Math Object:

Definition

Major Section:

Reference

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## Mathematics Subject Classification

15A63*no label found*12D15

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