Fernando Galván, José Francisco (2002) Sums of squares in real analytic rings. Transactions of the American Mathematical Society, 354 (5). pp. 1909-1919. ISSN 0002-9947
![[img]](http://eprints.ucm.es/style/images/fileicons/application_pdf.png) |
PDF
Restricted to Repository staff only until 2020. 197kB |
Official URL: http://www.ams.org/journals/tran/2002-354-05/S0002-9947-02-02956-
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.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | Analytic ring; Positive semidefnite element; Sum of squares; Pythagoras number. |
| Subjects: | Sciences > Mathematics > Number theory Sciences > Mathematics > Algebraic geometry |
| ID Code: | 15238 |
| References: | 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). |
| Deposited On: | 17 May 2012 08:08 |
| Last Modified: | 06 Feb 2014 10:19 |
Repository Staff Only: item control page
