When \(\varphi(f)\) convergent implies \(f\) is convergent

DOI10.1007/BF01391465zbMath0355.13010MaRDI QIDQ1237101

Gary A. Harris, Paul M. jun. Eakin

Publication date: 1977

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/163016

Mathematics Subject Classification ID

Complete rings, completion (13J10) Power series rings (13J05) Analytic algebras and generalizations, preparation theorems (32B05)

Related Items (21)

Division and composition theorems in the ring of analytic Dirichlet series. ⋮ Gabrielov's rank condition is equivalent to an inequality of reduced orders ⋮ Homomorphisms of local algebras in positive characteristic ⋮ The Traces of Holomorphic Functions on Real Submanifolds ⋮ Monomialization of a quasianalytic morphism ⋮ Automorphism groups of minimal real-analytic CR manifolds ⋮ Unnamed Item ⋮ On composite formal power series ⋮ Arc-smooth functions on closed sets ⋮ Homomorphism of quasianalytic local rings ⋮ Linear nested Artin approximation theorem for algebraic power series ⋮ Analytic and polynomial homomorphisms of analytic rings ⋮ Linear Chevalley Estimates ⋮ Formal versus analytic CR mappings ⋮ Applications of functional analysis to the solution of power series equations ⋮ Solving power series equations. II: Change of ground field ⋮ A proof of A. Gabrielov's rank theorem ⋮ The rank condition and convergence of formal functions ⋮ Note on linear chevalley estimate for homomorphisms of local algebras ⋮ Unnamed Item ⋮ Link between Noetherianity and the Weierstrass Division Theorem on some quasianalytic local rings

Cites Work

• Two Notes on Formal Power Series
• FORMAL RELATIONS BETWEEN ANALYTIC FUNCTIONS
• Unnamed Item
• Unnamed Item

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