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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 analytic rings


Author: José F. Fernando
Journal: Trans. Amer. Math. Soc. 354 (2002), 1909-1919
MSC (2000): Primary 11E25; Secondary 14P15
Published electronically: January 10, 2002
MathSciNet review: 1881023
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Abstract: Let $A$ be an analytic ring. We show: (1) $A$ has finite Pythagoras number if and only if its real dimension is $\leq 2$, and (2) if every positive semidefinite element of $A$ is a sum of squares, then $A$ is real and has real dimension $2$.


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Additional Information

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

DOI: http://dx.doi.org/10.1090/S0002-9947-02-02956-2
PII: S 0002-9947(02)02956-2
Keywords: Analytic ring, positive semidefinite element, sum of squares, Pythagoras number
Received by editor(s): March 29, 2001
Received by editor(s) in revised form: August 14, 2001
Published electronically: January 10, 2002
Additional Notes: Research partially supported by DGICYT, PB98-0756-C02-01
Article copyright: © Copyright 2002 American Mathematical Society