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Separable ℵ k -free modules with almost trivial dual

Daniel Herden, Héctor Gabriel Salazar Pedroza (2016)

Commentationes Mathematicae Universitatis Carolinae

An R -module M has an almost trivial dual if there are no epimorphisms from M to the free R -module of countable infinite rank R ( ω ) . For every natural number k > 1 , we construct arbitrarily large separable ℵ k -free R -modules with almost trivial dual by means of Shelah’s Easy Black Box, which is a combinatorial principle provable in ZFC.

Separating ideals in dimension 2.

James J. Madden, Niels Schwartz (1997)

Revista Matemática de la Universidad Complutense de Madrid

Experience shows that in geometric situations the separating ideal associated with two orderings of a ring measures the degree of tangency of the corresponding ultrafilters of semialgebraic sets. A related notion of separating ideals is introduced for pairs of valuations of a ring. The comparison of both types of separating ideals helps to understand how a point on a surface is approached by different half-branches of curves.

Séries formelles et produit de Hadamard

Abdelkader Necer (1997)

Journal de théorie des nombres de Bordeaux

Nous nous intéressons ici essentiellement à l’algèbre de Hadamard des séries formelles. Si des résultats importants ont été obtenus dans le cas d’une variable, il n’en est pas de même dans le cas de plusieurs variables. En effet, beaucoup de problèmes posés restent encore sans réponse. C’est le cas par exemple du problème du quotient de Hadamard, ou celui de la caractérisation des éléments de Hadamard inversibles, ou les diviseurs de zéro, ou encore le problème des multiplicateurs de certains sous-ensembles...

Simple zeropotent paramedial groupoids are balanced

Robert El Bashir, Jaroslav Ježek, Tomáš Kepka (2000)

Czechoslovak Mathematical Journal

This short note is a continuation of and and its purpose is to show that every simple zeropotent paramedial groupoid containing at least three elements is strongly balanced in the sense of .

Solutions d'un système d'équations analytiques réelles et applications

Jean-Claude Tougeron (1976)

Annales de l'institut Fourier

On démontre que toute solution formelle y ‾ ( x ) d’un système d’équations analytiques réelles (resp. polynomiales réelles) f ( x , y ) = 0 , se relève en une solution C ∞ homotope à une solution analytique (resp. à une solution de Nash) aussi proche que l’on veut de y ‾ ( x ) pour la topologie de Krull. On utilise ce théorème pour démontrer l’algébricité (ou l’analyticité) de certains idéaux de R { x } (ou R [ [ x ] ] ), et aussi pour construire des déformations analytiques de germes d’ensembles analytiques en germes d’ensembles de Nash.

Solving power series equations. II. Change of ground field

Joseph Becker (1979)

Annales de l'institut Fourier

We study the effect of changing the residue field, on the topological properties of local algebra homomorphisms of analytic algebras (quotients of convergent power series rings). Although injectivity is not preserved, openness and closedness in the Krull topology, simple topology, and inductive topology is preserved.

Spaces of polynomial functions of bounded degrees on an embedded manifold and their duals

Shuzo Izumi (2015)

Annales Polonici Mathematici

Let (U) denote the algebra of holomorphic functions on an open subset U ⊂ ℂⁿ and Z ⊂ (U) its finite-dimensional vector subspace. By the theory of least spaces of de Boor and Ron, there exists a projection b from the local ring n , b onto the space Z b of germs of elements of Z at b. At a general point b ∈ U its kernel is an ideal and b induces the structure of an Artinian algebra on Z b . In particular, this holds at points where the kth jets of elements of Z form a vector bundle for each k ∈ ℕ. For an embedded...

Spectral Real Semigroups

M. Dickmann, A. Petrovich (2012)

Annales de la faculté des sciences de Toulouse Mathématiques

The notion of a real semigroup was introduced in [8] to provide a framework for the investigation of the theory of (diagonal) quadratic forms over commutative, unitary, semi-real rings. In this paper we introduce and study an outstanding class of such structures, that we call spectral real semigroups (SRS). Our main results are: (i) The existence of a natural functorial duality between the category of SRSs and that of hereditarily normal spectral spaces; (ii) Characterization of the SRSs as the...

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