Real Algebraic and Analytic Geometry

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21. José F. Fernando, Jesús M. Ruiz, Claus Scheiderer:
Sums of squares in real rings.

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Submission: 2002, October 25.

Let $A$ be an excellent ring. We show that if the real dimension of $A$ is $\geq 3$ then $A$ has infinite Pythagoras number and there exist positive semidefinite elements in $A$ which are not sum of squares on $A$.

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