Talk:Pythagorean field
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Ito
[edit]The Ito reference does not seem to work. Tkuvho (talk) 05:26, 1 March 2011 (UTC)
Finding mistakes
[edit]Here it says that
- F is the intersection of its Euclidean closures.[1]
but if F is not ordered, then it doesn't have any Euclidean closures.
- If ab is not a square in F then there is an order on F for which a, b have different signs.[2]
But if F is the complex numbers, then it doesn't have any such order.
- The general u-invariant u(F) is 0 or 1.[3]
I've looked at the definitions, and this should in fact be infinity when F is the real numbers. I'm not as sure of this, so somebody ought to check. The definition of general u-invariant is stated unclearly, but if you understand an element of a Witt group to be a coset consisting of quadratic forms, then for F = real numbers, I think the value of u(F) is indeed 0. --Svennik (talk) 15:30, 22 June 2023 (UTC)
Svennik (talk) 15:30, 22 June 2023 (UTC)
Can somebody verify the exact sequence?
[edit]Since I've found other mistakes in that section, I'm wondering if the exact sequence is a true one. It might well be, but somebody should check. Somebody should also follow the citations because other incorrect claims in this article have been backed up by (mis-)citations. --Svennik (talk) 15:40, 22 June 2023 (UTC)
- The "Witt rings" here are really groups. Since this is an exact sequence of abelian groups, it should say Witt group. --Svennik (talk) 16:31, 22 June 2023 (UTC)