Publication:
Sums of squares in real analytic rings.

Loading...
Thumbnail Image
Full text at PDC
Publication Date
2002
Advisors (or tutors)
Editors
Journal Title
Journal ISSN
Volume Title
Publisher
American Mathematical Society
Citations
Google Scholar
Research Projects
Organizational Units
Journal Issue
Abstract
Let A be an analytic ring. We show:(1) A has finite Pythagoras number if and only if its real dimension is 2, and (2) if every positive semidefinite element of A is a sum of squares, then A is real and has real dimension 2.
Description
Keywords
Citation
C. Andradas, L. Br�ocker, J.M. Ruiz:Constructible sets in real geometry. Ergeb. Math.33. Berlin Heidelberg New York: Springer Verlag, 1996. MR 98e:14056 C. Andradas, J.M. Ruiz: On local uniformization of orderings. In Recent advances in real algebraic geometry and quadratic forms, Proceedings of the RAGSQUAD Year,Berkeley 1990-1991. AMS Contemporary Math. 155, 19-46 (1994). MR 94k:14048 J. Bochnak, M. Coste, M.F. Roy: Real Algebraic Geometry, Ergeb. Math. 36 Berlin Heidelberg New York: Springer-Verlag, 1998. MR 2000a:14067 A. Campillo, J.M. Ruiz: Some Remarks on Pythagorean Real Curve Germs, J. Algebra 128, No. 2, 271-275 (1990). MR 91b:14072 M.D. Choi, Z.D. Dai, T.Y. Lam, B. Reznick: The Pythagoras number of some ane algebras and local algebras, J. Reine Angew. Math. 336, 45-82 (1982). MR 84f:12012 J.F. Fernando: Positive semidenite germs in real analytic surfaces, Math. Ann. (to appear). J.F. Fernando: On the Pythagoras numbers of real analytic rings, J. Algebra 243,321-338 (2001). CMP 2001:17 J.F. Fernando: Analytic surface germs with minimal J.F. Fernando, J.M. Ruiz: Positive semidenite germs on the cone, Pacic J. Math. (to appear). T. de Jong, G. Pster: Local Analytic Geometry, basic theory and applications,Advanced Lectures in Mathematics. Braunschweig/Wiesbaden: Vieweg, 2000. MR 2001c:32001 J. Ortega: On the Pythagoras number of a real irreducible algebroid curve, Math. Ann. 289, 111-123 (1991). MR 92a:14065 R. Quarez: Pythagoras numbers of real algebroid curves and Gram matrices. J. Algebra 238, 139-158 (2001). J.M. Ruiz: On Hilbert's 17th problem and real nullstellensatz for global analytic functions,Math. Z. 190, 447-459 (1985). MR 87b:32010 J.M. Ruiz: The basic theory of power series, Advanced Lectures in Mathematics.Braunschweig Wiesbaden: Vieweg Verlag, 1993. MR 94i:13012 J.M. Ruiz: Sums of two squares in analytic rings, Math. Z. 230, 317-328 (1999). MR 2000b:58068 C. Scheiderer: Sums of squares of regular functions on real algebraic varieties, Trans.Amer. Math. Soc. 352, nr. 3, 1039-1069 (1999). MR 2000j:14090 C. Scheiderer: On sums of squares in local rings, J. Reine Angew. Math. 540, 205{227 (2001).
Collections