Tougeron, Jean-Claude Inégalités de Lojasiewicz globales. (Global Lojasiewicz inequalities). (French) Zbl 0748.32007 Ann. Inst. Fourier 41, No. 4, 841-866 (1991). On étudie les propriétés métriques des ensembles analytiques réels \(f=0\), avec \(f\in{\mathcal O}(\Omega)\), \({\mathcal O}(\Omega)\) algèbre analytique topologiquement noethérienne. Ainsi, on construit de larges classes d’algèbres \({\mathcal O}(\Omega)\) topologiquement nothériennes et vérifiant des conditions de Łojasiewicz globales d’un certain type. Comme application, on obtient des théorèmes de division de fonctions \(C^ \infty\) par des fonctions analytiques. Reviewer: J.-C.Tougeron Cited in 5 Documents MSC: 32B05 Analytic algebras and generalizations, preparation theorems 26E10 \(C^\infty\)-functions, quasi-analytic functions 32A38 Algebras of holomorphic functions of several complex variables Keywords:Lojasiewicz inequality; finite growth PDFBibTeX XMLCite \textit{J.-C. Tougeron}, Ann. Inst. Fourier 41, No. 4, 841--866 (1991; Zbl 0748.32007) Full Text: DOI Numdam EuDML References: [1] L. HORMANDER, On the division of distributions by polynomials, Arks Mat., 3 (1958). · Zbl 0131.11903 [2] B. MALGRANGE, Ideals of differentiable functions, Oxford Univ. Press, 1966. · Zbl 0177.17902 [3] J. Cl. TOUGERON, Algèbres analytiques topologiquement nthériennes, Annales de l’Institut Fourier, 41-4 (1991), 823-840. · Zbl 0786.32011 [4] J. Cl. TOUGERON, Sur certaines algèbres de fonctions analytiques, Séminaire de géométrie algébrique réelle, Paris VII (1986). · Zbl 0634.14017 [5] J. Cl. TOUGERON, Familles nthériennes de modules sur k[[x]] et applications, Preprint Rennes (1985). This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.