Sums of squares in real rings

Fernando, José; Ruiz, Jesús; Scheiderer, Claus

doi:10.1090/S0002-9947-03-03438-X

Sums of squares in real rings
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by José F. Fernando, Jesús M. Ruiz and Claus Scheiderer PDF

Trans. Amer. Math. Soc. 356 (2004), 2663-2684 Request permission

Abstract:

Let $A$ be an excellent ring. We show that if the real dimension of $A$ is at least three then $A$ has infinite Pythagoras number, and there exists a positive semidefinite element in $A$ which is not a sum of squares in $A$.

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