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Autor Ruiz Sancho, Jesús María |
Documentos disponibles escritos por este autor (73)
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A set which can be defined by systems of polynomial inequalities is called semialgebraic. When such a scription is possible locally around every point, by means of analytic inequalities varying with the point, the set; is called semianalytic. If[...]![]()
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A semialgebraic set is called basic if it can be described by a single system of strict polynomial inequalities. A semianalytic set is called basic if it can be described by a system of strict real analytic inequalities in a neighborhood of each[...]![]()
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Let ??Rn be a compact Nash manifold; A,B the rings of Nash, analytic global functions on ?. The main result of this paper is the following: Theorem 1. Let ?,?? be a pair of Nash submanifolds of some Rn ,Rq and let us suppose ? is compact. Let F1[...]![]()
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Baro González, Elías ; Fernando Galván, José Francisco ; Ruiz Sancho, Jesús María | Elsevier | 2014-09This paper is devoted to the approximation of differentiable semialgebraic functions by Nash functions. Approximation by Nash functions is known for semialgebraic functions defined on an affine Nash manifold M, and here we extend it to functions[...]![]()
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We give an expository account of the basic features of analytic and semianalytic germs. The main results treated here are Risler's Nullstellensatz, the curve selection lemma and the finiteness theorem for semianalytic germs. The method of proof [...]![]()
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Abánades, Miguel A. ; Joglar-Prieto, Nuria ; Ruiz Sancho, Jesús María | Elsevier Science B.V. (North-Holland) | 1999-10-01We show that the ring of bounded meromorphic functions on an irreducible compact real analytic set of dimension d is a Prüfer domain of dimension d. Consequently, every finitely generated ideal in this ring can be generated by d + 1 elements, an[...]![]()
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The paper deals with orderings in the field K(X0) of meromorphic function germs on an irreducible analytic germ X0?Rn0 of dimension d. It is inspired by the theory of central points of real algebraic varieties (the set of central points is the c[...]![]()
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Hilbert's 17th Problem asked the following. Let f(x1,?,xn) be a real polynomial which for all real values ?1,?,?n satisfies f(?1,?,?n)?0. Is it true that f=?(gi/hi)2 for polynomials gi,hi?R[x1,?,xn]? (It was known that f=?(gi)2, gi?R[x1,?,xn], i[...]![]()
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Let A be a local ring; let  denote the completion of A and Spec r A,Spec R  the real spectra of A and Â,respectively. The author studies the fibers of the canonical morphism Spec r  ? Spec r A, for an excellent ring A, and computes its images[...]![]()
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In this note, the author proves, in the context of excellent rings, two results on chains of specializations in the real spectrum and some corollaries about real dimension. The first result (Theorem I) is the following: let ?0 be a point of Spec[...]![]()
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En este trabajo obtemos algunos resultados básicos sobre determinación finita y clasificación de singularidades para series con coeficientes en un cuerpo de características cero. Estos resultados son clásicos para coeficientes complejos, y reale[...]![]()
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The paper contains a technical but useful theorem about stratification of semianalytic sets![]()
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Este texto está dedicado a la geometría analítica elemental del plano y del espacio, insistiendo en la distinción natural entre las nociones vectoriales, las afines y las euclídes. Tras recordar brevemente las operaciones básicas de escalares y [...]![]()
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Rodríguez Sanjurjo, José Manuel ; Ruiz Sancho, Jesús María | Addison-Wesley Iberoamericana España | 1998Este libro presenta, de modo directo y accesible, las nociones y los resultados básicos de la geometría proyectiva: variedades y aplicaciones proyectivas, razón doble, homografías y cuádricas. La exposición teórica se completa con notas históric[...]![]()
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This is a survey on the history of and the solutions to the basic global problems on Nash functions, which have been only recently solved, namely: separation, extension, global equations, Artin-Mazur description and idempotency, also noetheriann[...]![]()
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In this note, the author gives a proof of the following going-down theorem: If ?:A?B is a regular map between Noetherian rings with A excellent, any chain of specialization in Spec r A comes from a chain of the same length in Spec r B with corr[...]![]()
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Let X be a real affine algebraic set and S a semialgebraic set. Many important results are known about the basicness of S: mainly, if S is basic open, S can be defined by s strict inequalities, where s is bounded by the dimension of X. It is als[...]