Real Algebraic and Analytic Geometry
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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 $A$.
Full text: pdf=http://www.mat.ucm.es/~jesusr/pdfs/dim3.pdf