Showing papers in "Publicacions Matematiques in 1989"
TL;DR: In this article, the authors characterized a right zip ring by the property that every injective right module E is divisible by every left ideal L such that L^ = 0.
Abstract: Zelmanowitz [12] introduced the concept of ring, which we call right zip rings, with the defining properties below, which are equivalent:
(ZIP 1) If the right anihilator X^ of a subset X of R is zero, then X1^ = 0 for a finite subset X1 I X.
(ZIP 2) If L is a left ideal and if L^ = 0, then L1^ = 0 for a finitely generated left ideal L1 I L.
In [12], Zelmanowitz noted that any ring R satisfying the d.c.c. on anihilator right ideals (= dcc ^) is a right zip ring, and hence, so is any subring of R. He also showed by example that there exist zip rings which do not have dcc ^.
In paragraph 1 of this paper, we characterize a right zip by the property that every injective right module E is divisible by every left ideal L such that L^ = 0. Thus, E = EL. (It suffices for this to hold for the injective hull of R).
In paragraph 2 we show that a left and right self-injective ring R is zip iff R is pseudo-Frobenius (= PF). We then apply this result to show that a semiprime commutative ring R is zip iff R is Goldie.
In paragraph 3 we continue the study of commutative zip rings.
55 citations
TL;DR: In this article, an exposition of basic known local and global results on Lagrangian foliations such as the Theorem of Darboux-Lie, Weinstein, Arnold-Liouville, etc.
Abstract: The paper is an exposition of basic known local and global results on Lagrangian foliations such as the Theorem of Darboux-Lie, Weinstein, Arnold-Liouville, a global characterization of cotangent bundles, higher order Maslov classes, etc.
26 citations
TL;DR: In this paper, the foliated version of Moser's lemma is used to study the isotopy classes of Poisson structures in relation with their cohomology class, and explicit examples with dim F = 2 are described.
Abstract: Regular Poisson structures with fixed characteristic foliation F are described by means of foliated symplectic forms. Associated to each of these structures, there is a class in the second group of foliated cohomology H2(F). Using a foliated version of Moser's lemma, we study the isotopy classes of these structures in relation with their cohomology class. Explicit examples, with dim F = 2, are described.
25 citations
TL;DR: In this article, an unpublished theorem of G. Duminy, on the topology of semiproper exceptional leaves, is extended to every leaf of a Markov LMS and other topological results on these leaves are also obtained.
Abstract: The authors continue their study of exceptional local minimal sets with holonomy modeled on symbolic dynamics (called Markov LMS [C-C 1]). Here, an unpublished theorem of G. Duminy, on the topology of semiproper exceptional leaves, is extended to every leaf, semiproper or not, of a Markov LMS. Other topological results on these leaves are also obtained.
15 citations
TL;DR: The existence of a versal space of deformations for complex structures on a Lie group invariant by a cocompact subgroup has been shown in this article for transversely holomorphic foliation on compact manifold.
Abstract: Let F be a transversely holomorphic foliation on a compact manifold. We show the existence of a versal space for those deformations of F which keep fixed its differentiable type if F is Hermitian or if F has complex codimension one and admits a transverse projectable connection. We also prove the existence of a versal space of deformations for the complex structures on a Lie group invariant by a cocompact subgroup.
14 citations
TL;DR: In this paper, it was shown that the loop space of a connected CW-complex is a P-local group, up to homotopy, if and only if p1X and the free homotoopy groups [Sk-1, OX], k = 2, are p-local.
Abstract: When localizing the semidirect product of two groups, the effect on the factors is made explicit. As an application in Topology, we show that the loop space of a based connected CW-complex is a P-local group, up to homotopy, if and only if p1X and the free homotopy groups [Sk-1, OX], k = 2, are P-local.
12 citations
TL;DR: In this paper, the role of unimodular functions in deciding the uniform boundedness of sets of continuous linear functionals on various function spaces was studied, and it was shown that inner functions are a UBD-set in H8 with the weak-star topology.
Abstract: In this paper we study the role that unimodular functions play in deciding the uniform boundedness of sets of continuous linear functionals on various function spaces. For instance, inner functions are a UBD-set in H8 with the weak-star topology.
10 citations
TL;DR: In this paper, an elementary proof of the following theorem is given: if the Euler-Poincare characteristic of a compact connected surface is non zero, then there exists a fixed point.
Abstract: An elementary proof of the following theorem is given:
THEOREM Let M be a compact connected surface without boundary Consider a C8 action of Rn on M Then, if the Euler-Poincare characteristic of M is non zero there exists a fixed point
10 citations
TL;DR: In this paper, the authors defined the 8-degree of sufficiency as the smallest integer r such that for any germ f such that f = g, there is a set of disjoint annuli in S3 whose boundaries consist of a component of the link of f and another component of g.
Abstract: Let f be a germ of plane curve, we define the 8-degree of sufficiency offto be the smallest integer r such that for any germ g such that j(r)f = j(r)g then there is a set of disjoint annuli in S3 whose boundaries consist of a component of the link of f and a component of the link of g. We establish a formula for the 8-degree of sufficiency in terms of link invariants of plane curves singularities and, as a consequence of this formula, we obtain that the 8-degree of sufficiency is equal to the C° -degree of sufficiency
7 citations
TL;DR: In this article, the authors gave a new condition on a monoid M for the monoid ring F[M] to be a 2-fir ring, which is the condition that the group of units of M is trivial, but M is not a directed union of free monoids.
Abstract: We give a new condition on a monoid M for the monoid ring F[M] to be a 2-fir. Furthermore, we construct a monoid M that satisfies all the currently known necessary conditions for F[M] to be a semifir and that the group of units of M is trivial, but M is not a directed union of free monoids.
TL;DR: In this paper, the authors give a criterium for an unfolding of a holomorphic foliation with singularities to be holomorphically trivial, where singularity is defined as the number of singularities in the foliation.
Abstract: The objective of this paper is to give a criterium for an unfolding of a holomorphic foliation with singularities to be holomorphically trivial.
TL;DR: In this article, the Thom isomorphism of C *-algebras of foliations has been proved for all C 0-foliations without holonomy on a closed manifold.
Abstract: In [C2], Baum-Connes state a conjecture for the K-theory of C*-algebras of foliations. This conjecture has been proved by T. Natsume [N2] for C8-codimension one foliations without holonomy on a closed manifold. We propose here another proof of the conjecture for this class of foliations, more geometric and based on the existence of the Thom isomorphism, proved by A. Connes in [C3]. The advantage of this approach is that the result will be valid for all C0-foliations.
TL;DR: In this article, a nonlinear parabolic system with Dirichlet boundary conditions and initial data is considered, and it is shown that, for tn→ + ∞, the solution of (S) converges to some solution of the elliptic system associated with (S).
Abstract: Let us consider a nonlinear parabolic system of the following type: [la formula corresponent es troba al document] with Dirichlet boundary conditions and initial data. In this paper, we construct sub-supersolutions of (S), and by use of them, we prove that, for tn→ +∞, the solution of (S) converges to some solution of the elliptic system associated with (S).
TL;DR: In this article, it was shown that every closed subset of CN that has finite (2N - 2)-dimensional measure is a removable set for holomorphic functions, and a related result on the ball was obtained.
Abstract: We show that every closed subset of CN that has finite (2N - 2)-dimensional measure is a removable set for holomorphic functions, and we obtain a related result on the ball.
TL;DR: In this paper, the shape of the free-boundary and the localization of the cavited region of a cylindrical bearing were investigated. But the shape was not characterized.
Abstract: The hidrodynamic lubrication of a cylindrical bearing is governed by the Reynolds equation that must be satisfied by the preassure of lubricatiog oil. When cavitation occurs we are carried to an elliptic free-boundary problem where the free-boundary separates the lubricated region from the cavited region. Some qualitative properties are obtained about the shape of the free-boundary as well as the localization of the cavited region.
TL;DR: In this article, the authors prove the existence of a symplectic realization for a large class of regular Poisson manifolds with Riemannian two-dimensional characteristic foliation, and show that the homotopy groupoid of such a foliation is locally trivial.
Abstract: The purpose of this paper is to prove the existence of a symplectic realization for a large class of regular Poisson manifolds with Riemannian two dimensional characteristic foliation. To do so, we will show that the homotopy groupoid of a Riemannian foliation is locally trivial.
TL;DR: In this article, the authors find some conditions that ensure that a G foliation of finite type with all leaves compact is a Riemannian foliation and equivalently the space of leaves of such a foliation is a Satake manifold.
Abstract: In this short note we find some conditions which ensure that a G foliation of finite type with all leaves compact is a Riemannian foliation of equivalently the space of leaves of such a foliation is a Satake manifold. A particular attention is paid to transversaly affine foliations. We present several conditions which ensure completeness of such foliations.
TL;DR: In this article, the authors give an example of a singular Poisson structure on R2 which admits a symplectic realization by a Lie groupoid, and show how to construct such a structure.
Abstract: The purpose of this note is to give an example of a singular Poisson structure on R2 which admits a symplectic realization by a Lie groupoid.
TL;DR: In this paper, it was shown that Martin's axiom and the negation of the Continuum Hypothesis imply that the product of ccc spaces is a ccc space.
Abstract: In this expository paper it is shown that Martin's Axiom and the negation of the Continuum Hypothesis imply that the product of ccc spaces is a ccc space. The Continuum Hypothesis is then used to construct the Laver-Gavin example of two ccc spaces whose product is not a ccc space.
TL;DR: In this paper, the construction of the fundamental groupoid and the homotopy groupoid associated to foliations with Reeb components were studied. And they were shown to be Hausdorff spaces.
Abstract: Let M be a manifold with a regular foliation F. We recall the construction of the fundamental groupoid and the homotopy groupoid associated to F. We describe some interesting particular cases and give some glueing techniques. We characterize the cases where these groupoids are Hausdorff spaces.
We study in particular both groupoids associated to foliations with Reeb components.
TL;DR: In this article, it was shown that if R is left perfect ring (resp. semiperfect ring) then every [r] f Є R-tors/F (resp., [X]F and [e]F) is a complete sublattice of R-Tors.
Abstract: We define F in R-tors by r F σ iff the class of r-codivisible modules coincides with the class of σ -codivisible modules. We prove that if R is left perfect ring (resp. semiperfect ring) then every [r] f Є R-tors/ F (resp. [X]F and [e]F) is a complete sublattice of R-tors We describe the largest element in [r] as X(Rad R/t,(Rad R)) and the least element of [r] as e (t r(RadR)) Using these results we give a necessary and sufficient condition for the central splitting of Goldman torsion theory when R is semiperfect. We prove that for a QF ring R the least element of [X] F is the Goldie torsion theory. This can be used to prove that for a QF ring F and T are equal, where r T o iff the class of r-injective modules coincides with the class of σ-injective modules .
TL;DR: For a wide class of N functions o 0, the ergodic maximal operator associated to T is bounded in L o as discussed by the authors, and for every f € L o we have the almost everywhere convergence and the norm convergente of certain weighted averages which include the Cesaro averages.
Abstract: Let (X, M,ų) be a σ-finite measure space, Lo - Lo (X, M, ų) an Orlicz space associated to an N-function o and let T : Lo→Lo be a linear operator with a fixed point h ≠ 0 a.e ., such that [formula matematica inclosa a l’article] and it is either a II 1 -contraction in Lo ∩ L1 or a II II∞ .-contraction in Lo ∩ L∞ The main result of this paper is that for a wide class of N functions o 0, the ergodic maximal operator associated to T is bounded in L o. Moreover, for every f € L o we have the almost everywhere convergence and the norm convergente of certain weighted averages which include the Cesaro averages.
TL;DR: The Weitzenbock formulae express the Laplacian of a differential form on an oriented Riemannian manifold in local coordinates, using the covariant derivatives of the form and the coefficients of the curvature tensor as discussed by the authors.
Abstract: The Weitzenbock formulae express the Laplacian of a differential form on an oriented Riemannian manifold in local coordinates, using the covariant derivatives of the form and the coefficients of the curvature tensor. In the first part, we shall describe a certain "differential algebra formalism" which seems to be a more natural frame for those formulae than the usual calculations in local coordinates. In this formalism, there appear some interesting differential operators which may also be used to characterize local geometric properties of foliations. That is the topic of the second part.
TL;DR: In this paper, it was shown that a polynomial ring R[x] over a SISI ring R is not again SisI. In this paper, we show that this is not the case.
Abstract: All rings considered are commutative with unit. A ring R is SISI (in Vamos' terminology) if every subdirectly irreducible factor ring R/I is self-injective. SISI rings include Noetherian rings, Morita rings and almost maximal valuation rings ([V1]). In [F3] we raised the question of whether a polynomial ring R[x] over a SISI ring R is again SISI. In this paper we show this is not the case.
TL;DR: In this article, the phase portraits of the cubic systems in the plane such that they do not have finite critical points, and the critical points on the equator of the Poincare sphere are isolated and have linear part non-identically zero.
Abstract: We classify the phase portraits of the cubic systems in the plane such that they do not have finite critical points, and the critical points on the equator of the Poincare sphere are isolated and have linear part nonidentically zero.
TL;DR: In this paper, the authors give the links between singular foliations, G-structures and momentum mapping in the context of symplectic geometry, and show that the notions of singular foliation and G-structure are related.
Abstract: One gives the links between the notions of singular foliations, G-structures and momentum mapping in the context of symplectic geometry.
TL;DR: In this article, the phase portraits of the cubic systems in the plane such that they do not have finite critical points, and the critical points on the equator of the Poincare sphere are isolated and have linear part non-identically zero.
Abstract: We classify the phase portraits of the cubic systems in the plane such that they do not have finite critical points, and the critical points on the equator of the Poincare sphere are isolated and have linear part non-identically zero.
TL;DR: In this paper, the problem of determining the order of the Whitehead square is posed and some computations are given, where direct relations between the generalized Whitehead product for track groups and the generalized whitehead product in the sense of Arkowitz are shown.
Abstract: Two direct relations are exhibited between the Whitehead product for track groups studied in [4] and the generalized Whitehead product in the sense of Arkowitz. The problem of determining the order of the Whitehead square is posed and some computations given.
TL;DR: In this paper, the authors studied the ramification divisors of the functions in M(v') which have exponential singularities of finite degree at the points of v-v', and proved that for a given finite divisor d in v', the functions of the said type whose divisori id d, define a proper analytic subset of a certain symmetric power of v'.
Abstract: Let v be a compact Riemann surface and v' be the complement in v of a nonvoid finite subset. Let M(v') be the field of meromorphic functions in v'. In this paper we study the ramification divisors of the functions in M(v') which have exponential singularities of finite degree at the points of v-v', and one proves, for instance, that if a function in M(v') belongs to the subfield generated by the functions of this type, and has a finite ramification divisor, it also has a finite divisor. It is also proved that for a given finite divisor d in v', the ramification divisors (with a fixed degree) of the functions of the said type whose divisor id d, define a proper analytic subset of a certain symmetric power of v'.