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# Linear nested Artin approximation theorem for algebraic power series Linear nested Artin approximation theorem for algebraic power series
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 Author: Castro Jiménez, Francisco Jesús Popescu, Dorin Rond, Guillaume Department: Universidad de Sevilla. Departamento de álgebra Date: 2018 Published in: Manuscripta mathematica, 1-19. Document type: Article Abstract: We give an elementary proof of the nested Artin approximation Theorem for linear equations with algebraic power series coefficients. Moreover, for any Noetherian local subring of the ring of formal power series, we clarify the relationship between this theorem and the problem of the commutation of two operations for ideals: the operation of replacing an ideal by its completion and the operation of replacing an ideal by one of its elimination ideals. In particular we prove that a Grothendieck conjecture about morphisms of analytic/formal algebras and Artin’s question about linear nested approximation problem are equivalent.
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DOI: 10.1007/s00229-018-1025-0 This work is under a Creative Commons License:
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