Approximation results of Artin-Tougeron-type for general filtrations and for C^r-equations

2019/07/23 by Belitskii, Genrich, Boix, Alberto F., Kerner, Dmitry · 1 citation
#Commutative Algebra (math.AC) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1907.09736

Abstract

Artin approximation and other related approximation results are used in various areas. The traditional formulation of such results is restricted to filtrations by powers of ideals, \I^j\, and to Noetherian rings. In this paper we extend several approximation results both to rather general filtrations and to C^r-rings, for 2≤ r≤∞. As an auxiliary step we establish the surjectivity of the completion map for rings of C^∞ functions, for a very broad class of filtrations.

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