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On the Pythagoras numbers of real analytic rings

dc.contributor.authorFernando Galván, José Francisco
dc.date.accessioned2023-06-20T16:51:21Z
dc.date.available2023-06-20T16:51:21Z
dc.date.issued2001
dc.description.abstractWe show that the Pythagoras number of a real analytic ring of dimension 2 is finite, bounded by a function of the multiplicity and the codimension.
dc.description.departmentDepto. de Álgebra, Geometría y Topología
dc.description.facultyFac. de Ciencias Matemáticas
dc.description.refereedTRUE
dc.description.sponsorshipDGICYT, PB98
dc.description.statuspub
dc.eprint.idhttps://eprints.ucm.es/id/eprint/15239
dc.identifier.doi10.1006/jabr.2001.8869
dc.identifier.issn0021-8693
dc.identifier.officialurlhttp://www.sciencedirect.com/science/article/pii/S0021869301988696
dc.identifier.relatedurlhttp://www.sciencedirect.com/
dc.identifier.urihttps://hdl.handle.net/20.500.14352/57242
dc.issue.number1
dc.journal.titleJournal of Algebra
dc.language.isoeng
dc.page.final338
dc.page.initial321
dc.publisherAcademic Press
dc.relation.projectIDPB98-0756-C02-01
dc.rights.accessRightsrestricted access
dc.subject.cdu512.7
dc.subject.ucmGeometria algebraica
dc.subject.unesco1201.01 Geometría Algebraica
dc.titleOn the Pythagoras numbers of real analytic rings
dc.typejournal article
dc.volume.number243
dcterms.referencesC. Andradas, L. Br¨ocker, and J. M. Ruiz, “Constructible Sets in Real Geometry,”Ergeb. Math., Vol. 33, Springer-Verlag, Berlin/Heidelberg/New York, 1996. M. Artin, On the solution of analytic equations, Invent. Math. 5 (1968), 227–291. J. Bochnak, M. Coste, and M. F. Roy, “Real Algebraic Geometry,” Ergeb. Math.,Vol. 36, Springer-Verlag, Berlin/Heidelberg/New York, 1998. J. Bochnak, W. Kucharz, and M. Shiota, On equivalence of ideals of real global analytic functions and the 17th Hilbert problem, Invent. Math. 63 (1981), 403–421. J. Bochnak and J.-J. Risler, Le th´eor`eme des z´eros pour les vari´et’es analytiques r´eelles de dimension 2, Ann. Sci. Ecole Norm. Sup. 4 8 (1975), 353–364. J. W. S. Cassels, W. S. Ellison, and A. Pfister, On sums of squares and on elliptic curves over functions fields, J. Number Theory 3 (1971), 125–149. A. Campillo and J. M. Ruiz, Some remarks on Pythagorean real curve germs,J. Algebra 128 (1990), 271–275. M. D. Choi, Z. D. Dai, T. Y. Lam, and B. Reznick, The Pythagoras number of some affine algebras and local algebras, J. Reine Angew. Math. 336 (1982), 45–82. M. D. Choi, T. Y. Lam, and B. Reznick, Sums of squares of real polynomials, in Proc. Sympos. Pure. Math. Vol. 58, 103–126, Amer. Math. Soc., Providence, 1995. D. Z. Djokovi´c, Hermitian matrix over polynomial rings, J. Algebra 43 (1976),359–374. Ch. N. Diller and A. Dress, Zur Galoistheorie pythagor¨aischer K¨orper, Arch. Math.16 (1965), 148–152. J. F. Fernando, Positive semidefinite germs in real analytic surfaces, Mathematische Annalen, in press. J. F. Fernando, “Sumas de cuadrados en g´ermenes de superficie” Tesis doctoral,Universidad Complutense, Madrid, 2001. J. F. Fernando and J. M. Ruiz, Positive semidefinite germs on the cone, Pacific J.Math. in press.[Hu] T. W. Hungerford, “Algebra,” Grad. Text in Math., Vol. 73, Springer-Verlag,Berlin/New York, 1974. P. Jaworski, About estimates on number of squares necessary to represent a positive-semidefinite analytic function, Arch. Math. 58 (1992), 276–279. T. de Jong and G. Pfister, “Local Analytic Geometry, Basic Theory and Applications,”Advanced Lectures in Mathematics, Vieweg, Braunschweig/Wiesbaden,2000. E. Kunz, “Introduction to Commutative Algebra and Algebraic Geometry,”Birkh¨auser,Boston/Basel/Stuttgart,1985. H. Kurke, T. Mostowski, G. Pfister, D. Popescu, and M. Roczen, “Die Approximationseigenschaft lokaler Ringe,” Lecture Notes in Math., Vol. 634, Springer-Verlag,Berlin, 1978. S. Lang, “Algebra,” Addison–Wesley, Reading, MA, 1965. J. Ortega, On the Pythagoras number of a real irreducible algebroid curve, Math.Ann. 289 (1991), 111–123. A. Pfister, Zur Darstellung definiter Funktionen als Summe von Quadraten, Invent.Math. 4 (1967), 229–237. R. Quarez, Pythagoras numbers of real algebroid curves and Gram matrices,preprint, Univ. Rennes I, 1998. J. M. Ruiz, On Hilbert’s 17thproblem and real nullstellensatz for global analytic functions, Math. Z. 190 (1985), 447–449. J. M. Ruiz, “The Basic Theory of Power Series,” Advanced Lectures in Mathematics,Vieweg,Braunschweig/Wiesbaden, 1993. J. M. Ruiz, Sums of two squares in analytic rings, Math. Z. 230 (1999), 317–328. C. Scheiderer, On sums of squares in local rings, preprint, Univ. Duisburg, 2000. J. M. Ruiz, “The Basic Theory of Power Series,” Advanced Lectures in mathematics,Vieweg,Braunschweig/Wiesbaden, 1993. J. M. Ruiz, Sums of two squares in analytic rings, Math. Z. 230 (1999), 317–328. C. Scheiderer, On sums of squares in local rings, preprint, Univ. Duisburg, 2000.
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relation.isAuthorOfPublication.latestForDiscovery499732d5-c130-4ea6-8541-c4ec934da408

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