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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Sums of squares in real rings


Authors: José F. Fernando, Jesús M. Ruiz and Claus Scheiderer
Journal: Trans. Amer. Math. Soc. 356 (2004), 2663-2684
MSC (2000): Primary 14P99; Secondary 11E25, 32B10, 32S05
Published electronically: October 8, 2003
MathSciNet review: 2052192
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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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Additional Information

José F. Fernando
Affiliation: Departamento de Álgebra, Facultad Ciencias Matemáticas, Universidad Complutense de Madrid, 28040 Madrid, Spain
Email: josefer@mat.ucm.es

Jesús M. Ruiz
Affiliation: Departamento de Geometría y Topología, Facultad Ciencias Matemáticas, Universidad Complutense de Madrid, 28040 Madrid, Spain
Email: jesusr@mat.ucm.es

Claus Scheiderer
Affiliation: Institut für Mathematik, Fakultät 4, Universität Duisburg, 47048 Duisburg, Germany
Email: claus@uni-duisburg.de

DOI: http://dx.doi.org/10.1090/S0002-9947-03-03438-X
PII: S 0002-9947(03)03438-X
Received by editor(s): November 5, 2002
Published electronically: October 8, 2003
Additional Notes: All authors were supported by the European Research Training Network RAAG (HPRN-CT-2001-00271). The first and second named authors were also supported by the Spanish Research Project GAAR (BFM-2002-04797)
Article copyright: © Copyright 2003 American Mathematical Society