Sums of squares in real analytic rings.
| dc.contributor.author | Fernando Galván, José Francisco | |
| dc.date.accessioned | 2023-06-20T16:51:20Z | |
| dc.date.available | 2023-06-20T16:51:20Z | |
| dc.date.issued | 2002 | |
| dc.description.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. | |
| dc.description.department | Depto. de Álgebra, Geometría y Topología | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.refereed | TRUE | |
| dc.description.sponsorship | DGICYT | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/15238 | |
| dc.identifier.doi | 10.1090/S0002-9947-02-02956-2 | |
| dc.identifier.issn | 0002-9947 | |
| dc.identifier.officialurl | http://www.ams.org/journals/tran/2002-354-05/S0002-9947-02-02956- | |
| dc.identifier.relatedurl | http://www.ams.org/ | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/57241 | |
| dc.issue.number | 5 | |
| dc.journal.title | Transactions of the American Mathematical Society | |
| dc.language.iso | eng | |
| dc.page.final | 1919 | |
| dc.page.initial | 1909 | |
| dc.publisher | American Mathematical Society | |
| dc.relation.projectID | PB98-0756-C02-01 | |
| dc.rights.accessRights | restricted access | |
| dc.subject.cdu | 511 | |
| dc.subject.cdu | 512.7 | |
| dc.subject.keyword | Analytic ring | |
| dc.subject.keyword | Positive semidefnite element | |
| dc.subject.keyword | Sum of squares | |
| dc.subject.keyword | Pythagoras number. | |
| dc.subject.ucm | Teoría de números | |
| dc.subject.ucm | Geometria algebraica | |
| dc.subject.unesco | 1205 Teoría de Números | |
| dc.subject.unesco | 1201.01 Geometría Algebraica | |
| dc.title | Sums of squares in real analytic rings. | |
| dc.type | journal article | |
| dc.volume.number | 354 | |
| dcterms.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). | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | 499732d5-c130-4ea6-8541-c4ec934da408 | |
| relation.isAuthorOfPublication.latestForDiscovery | 499732d5-c130-4ea6-8541-c4ec934da408 |
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