A Bertini type theorem in analytic geometry.
A Cancellation Theorem for Artinian Local Algebras.
A Counterexample to Artin Approximation With Respect to Subrings.
A set on which the Łojasiewicz exponent at infinity is attained
We show that for a polynomial mapping the Łojasiewicz exponent of F is attained on the set .
Actions of Complex Lie Groups on Analytic ...-Algebras.
Algèbres analytiques topologiquement noéthériennes. Théorie de Khovanskii
On étudie certaines algèbres de fonctions analytiques réelles définies sur un ouvert de . La propriété principale de ces algèbres est que tout semi-analytique de défini globalement à l’aide d’un nombre fini de fonctions de , admet un nombre fini de composantes connexes. En reprenant les idées de Khovanskii (lemme de Rolle généralisé), on démontre que ces algèbres restent topologiquement noethériennes quand on leur adjoint les solutions de certaines équations différentielles du ler ordre. Par...
An elementary proof of the Briançon-Skoda theorem
We give an elementary proof of the Briançon-Skoda theorem. The theorem gives a criterionfor when a function belongs to an ideal of the ring of germs of analytic functions at ; more precisely, the ideal membership is obtained if a function associated with and is locally square integrable. If can be generated by elements,it follows in particular that , where denotes the integral closure of an ideal .
Analytic and Polynominal Homomorphisms of Analytic Rings.
Analytic curves in power series rings
Analytic deviation of ideals and intersection theory of analytic spaces.
Analytic rings
Applications of Functional Analysis to the Solution of Power Series Equations.