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 $A$.References
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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
- MR Author ID: 212893
- Email: claus@uni-duisburg.de
- 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)
- © Copyright 2003 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 356 (2004), 2663-2684
- MSC (2000): Primary 14P99; Secondary 11E25, 32B10, 32S05
- DOI: https://doi.org/10.1090/S0002-9947-03-03438-X
- MathSciNet review: 2052192