Sums of squares in real rings
| dc.contributor.author | Fernando Galván, José Francisco | |
| dc.contributor.author | Ruiz Sancho, Jesús María | |
| dc.contributor.author | Scheiderer, Claus | |
| dc.date.accessioned | 2023-06-20T09:33:45Z | |
| dc.date.available | 2023-06-20T09:33:45Z | |
| dc.date.issued | 2004 | |
| dc.description.abstract | Let A be an excellent ring. We show that if the real dimension of A is at least three then A has in finite Pythagoras number, and there exists a positive semidefinite element in A which is not a sum of squares in A. | |
| dc.description.department | Depto. de Álgebra, Geometría y Topología | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.refereed | TRUE | |
| dc.description.sponsorship | European Research Training Network RAAG | |
| dc.description.sponsorship | Spanish Research Project GAAR | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/15168 | |
| dc.identifier.doi | 10.1090/S0002-9947-03-03438-X | |
| dc.identifier.issn | 0002-9947 | |
| dc.identifier.officialurl | http://www.ams.org/journals/tran/2004-356-07/S0002-9947-03-03438-X/S0002-9947-03-03438-X.pdf | |
| dc.identifier.relatedurl | http://www.ams.org/ | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/49910 | |
| dc.issue.number | 7 | |
| dc.journal.title | Transactions of the American Mathematical Society | |
| dc.language.iso | eng | |
| dc.page.final | 2684 | |
| dc.page.initial | 2663 | |
| dc.publisher | American Mathematical Society | |
| dc.relation.projectID | HPRN-CT-2001-00271 | |
| dc.relation.projectID | BFM-2002-04797 | |
| dc.rights.accessRights | restricted access | |
| dc.subject.cdu | 512.7 | |
| dc.subject.cdu | 511 | |
| dc.subject.keyword | Positive semi-definite polynomial | |
| dc.subject.keyword | Excellent ring | |
| dc.subject.keyword | Real spectrum | |
| dc.subject.keyword | Complete local ring | |
| 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 rings | |
| dc.type | journal article | |
| dc.volume.number | 356 | |
| dcterms.references | C. Andradas, L. Br�ocker, J.M. Ruiz: Constructible Sets in Real Geometry. Ergeb. Math.Grenzgeb. 33. Berlin Heidelberg New York: Springer Verlag, 1996. MR 98e:14056 J. Bochnak, M. Coste, M.-F. Roy: Real Algebraic Geometry. Ergeb. Math. Grenzgeb. 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 128,271-275 (1990).MR 91b:14072 J.W.S. Cassels, W.J. Ellison, A. Pster: On sums of squares and on elliptic curves over function elds. J. Number Theory 3, 125-149 (1971). MR 45:1863 M.D. Choi, Z.D. Dai,T.Y. Lam,B.Reznick:ThePythagoras 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. 322,49-67(2002).MR 2003b:14069 J.F. Fernando: On the Pythagoras numbers of real analytic rings, J.Algebra 243, 321-338 (2001).MR 2002g:13051 J.F. Fernando: Analytic surface germs with minimal Pythagoras number, Preprint Univ.Complutense, Madrid 2002. J.F. Fernando: Sums of squares in real analytic rings, Trans. Am. Math. Soc. 354,1909-1919 (2002). MR2003b:14070 J.F. Fernando, J.M. Ruiz: Positive semidenite germs on the cone, Pacic J. Math. 205,109-118 (2002). MR 2003f:14066 J.F. Fernando, J.M. Ruiz: On the Pythagoras numbers of real analytic set germs (in preparation). T. de Jong, G. Pster: Local Analytic Geometry. Adv. Lect. Math. Braunschweig/Wiesbaden:Vieweg,2000.MR2001c:32001 H. Matsumura: Commutative Algebra, 2nd edition. London Amsterdam Tokyo: Benjamin,1980. MR 82i:13003 M. Nagata: Local Rings. New York London: John Wiley & Sons, 1962. MR 27:5790 J. Ortega: On the Pythagoras number of a real irreducible algebroid curve. Math. Ann.289, 111-123 (1991). MR 92a:14065 A. Pster: Quadratic Forms with Applications to Algebraic Geometry and Topology.London Math. Soc. Lect.Notes 217, Cambridge, 1995. MR 97c:11046 A. Prestel, C.N. Delzell: Positive Polynomials. Monographs in Mathematics. Berlin Heidelberg New York: Springer Verlag, 2001. MR 2002k:13044 R. Quarez: Pythagoras numbers of real algebroid curves and Gram matrices.J. Algebra 238,139-1582001).MR 2002g:14086 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: 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.Am. Math. Soc. 352,1039-1069 (1999).MR 2000j:14090 C. Scheiderer: On sums of squares in local rings, J. reine angew. Math. 540, 205-227(2001). MR 2002j:13031 C. Scheiderer: Sums of squares on real algebraic curves, Math. Z. (to appear)[Sch4] C. Scheiderer: Sums of squares on compact real algebraic surfaces (in preparation). | |
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