## Person: Gamboa Mutuberria, José Manuel

Loading...

##### First Name

José Manuel

##### Last Name

Gamboa Mutuberria

##### Affiliation

Universidad Complutense de Madrid

##### Faculty / Institute

Ciencias Matemáticas

##### Department

Álgebra, Geometría y Topología

##### Area

Álgebra

##### Identifiers

84 results

## Search Results

Now showing 1 - 10 of 84

Publication El espacio de órdenes de un cuerpo de funciones algebraicas de una variable(Universidad Complutense de Madrid, 2015) Gamboa Mutuberria, José Manuel; Recio Muñiz, TomásPublication El espacio de órdenes de funciones algebraicas de una variable(Universidad Complutense de Madrid, 2015) Gamboa Mutuberria, José ManuelPublication On the Krull dimension of rings of continuous semialgebraic functions(Universidad Autónoma Madrid, 2015) Fernando Galván, José Francisco; Gamboa Mutuberria, José ManuelLet R be a real closed field, S(M) the ring of continuous semialgebraic functions on a semialgebraic set M subset of R-m and S* (M) its subring of continuous semialgebraic functions that are bounded with respect to R. In this work we introduce semialgebraic pseudo-compactifications of M and the semialgebraic depth of a prime ideal p of S(M) in order to provide an elementary proof of the finiteness of the Krull dimensions of the rings S(M) and S* (M) for an arbitrary semialgebraic set M. We are inspired by the classical way to compute the dimension of the ring of polynomial functions on a complex algebraic set without involving the sophisticated machinery of real spectra. We show dim(S(M)) = dim(S* (M)) = dim(M) and prove that in both cases the height of a maximal ideal corresponding to a point p is an element of M coincides with the local dimension of M at p. In case p is a prime z-ideal of S(M), its semialgebraic depth coincides with the transcendence degree of the real closed field qf(S(M)/p) over RPublication On the semialgebraic Stone-Čech compactification of a semialgebraic set(American Mathematical Society, 2012) Fernando Galván, José Francisco; Gamboa Mutuberria, José ManuelIn the same vein as the classical Stone–ˇCech compactification, we prove in this work that the maximal spectra of the rings of semialgebraic and bounded semialgebraic functions on a semialgebraic set M ⊂ Rn, which are homeomorphic topological spaces, provide the smallest Hausdorff compactification of M such that each bounded R-valued semialgebraic function on M extends continuously to it. Such compactification β∗sM, which can be characterized as the smallest compactification that dominates all semialgebraic compactifications of M, is called the semialgebraic Stone– ˇ Cech compactification of M, although it is very rarely a semialgebraic set. We are also interested in determining the main topological properties of the remainder ∂M = β∗sM \M and we prove that it has finitely many connected components and that this number equals the number of connected components of the remainder of a suitable semialgebraic compactification of M. Moreover, ∂M is locally connected and its local compactness can be characterized just in terms of the topology of M.Publication On the spectra of rings of semialgebraic functions(Springer, 2012) Fernando Galván, José Francisco; Gamboa Mutuberria, José ManuelIn this article we study the most significant algebraic, topological and functorial properties of the Zariski and maximal spectra of rings of semialgebraic and bounded semialgebraic functions on a semialgebraic set.Publication On the number of ovals of a symmetry of a compact Riemann surface(Universidad Autónoma Madrid, 2008) Gamboa Mutuberria, José Manuel; Bujalance, E.; Cirre, Francisco; Gromadzki, G.The set of stationary points of the anticonformal involution (reflection) of a Riemann surface is called an oval. In this paper the total number of ovals of all reflections on a surface is counted provided the group of conformal automorphisms of the surface is cyclic. The bounds for this number are also given.Publication On the remainder of the semialgebraic Stone-Cech compactification of a semialgebraic set(Elsevier Science B.V. (North-Holland), 2018) Fernando Galván, José Francisco; Gamboa Mutuberria, José ManuelIn this work we analyze some topological properties of the remainder partial derivative M := beta(s)*M\M of the semialgebraic Stone-Cech compactification beta(s)*M of a semialgebraic set M subset of R-m in order to 'distinguish' its points from those of M. To that end we prove that the set of points of beta(s)*M that admit a metrizable neighborhood in beta(s)*M equals M-1c boolean OR (Cl beta(s)*M((M) over bar <= 1)\(M) over bar <= 1) where M-1c is the largest locally compact dense subset of M and (M) over bar <= 1 is the closure in M of the set of 1-dimensional points of M. In addition, we analyze the properties of the sets (partial derivative) over capM and (partial derivative) over tildeM of free maximal ideals associated with formal and semialgebraic paths. We prove that both are dense subsets of the remainder partial derivative M and that the differences partial derivative M\(partial derivative) over capM and (partial derivative) over capM\(partial derivative) over tildeM are also dense subsets of partial derivative M. It holds moreover that all the points of (partial derivative) over capM have countable systems of neighborhoods in beta(s)*M.Publication On the set of fixed points of automorphisms of bordered Klein surfaces(Universidad Autónoma Madrid, 2012) Gamboa Mutuberria, José Manuel; Gromadzki, G.The nature of the set of points fixed by automorphisms of Riemann or unbordered nonorientable Klein surfaces as well as quantitative formulae for them were found by Macbeath, Izquierdo, Singerman and Gromadzki in a series of papers. The possible set of points fixed by involutions of bordered Klein surfaces has been found by Bujalance, Costa, Natanzon and Singerman who showed that it consists of isolated fixed points, ovals and chains of arcs. They classified involutions of such surfaces, up to topological conjugacy in these terms. Here we give formulae for the number of elements of each type, also for non-involutory automorphisms, in terms of the topological type of the action of the group of dianalytic automorphisms. Finally we give some illustrative examples concerning bordered Klein surfaces with large groups of automorphisms already considered by May and Bujalance.Publication On the problem of finding the full automorphism group of a compact Klein surface(Universidad Complutense de Madrid, 2000) Cirre, F.J.; Gamboa Mutuberria, José ManuelThe paper under review surveys most known results about the following problem: let $X$ be a compact topological surface of algebraic genus $p>1$, with or without boundary, orientable or not. How to calculate all groups acting as the full automorphism group of some structure of Klein surface having $X$ as underlying topological surface? It must be remarked that from Riemann's uniformization theorem, and since $\Aut(X)$ has no more than 168 $(p-1)$ automorphisms (including the orientation-reversing ones), this problem is of a finite nature. In practice this is an unaccessible task except for low values of $p$ or some extra conditions on the surfaces one is dealing with.Publication Unbounded convex polyhedra as polynomial images of Euclidean spaces(2019) Fernando Galvan, José Francisco; Gamboa Mutuberria, José Manuel; Ueno Jacue, Carlos