%0 Unpublished work
%T LINEAR NESTED ARTIN APPROXIMATION THEOREM FOR ALGEBRAIC POWER SERIES
%+ Departamento de Algebra [Sevilla] (DALG-US)
%+ Institut de Mathématiques de Marseille (I2M)
%A Castro-Jiménez, Francisco-Jesus
%A Rond, Guillaume
%Z We have added a reference to a paper of E. Bierstone and P. Milman in which our Proposition 5.1 is proven.
%8 2015-12-07
%D 2015
%Z 1511.09275
%Z Mathematics [math]/Commutative Algebra [math.AC]
%Z Mathematics [math]/Algebraic Geometry [math.AG]Preprints, Working Papers, ...
%X We give a new and 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 com-mutation 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.
%G English
%2 https://hal.science/hal-01235349v2/document
%2 https://hal.science/hal-01235349v2/file/nested_linear-11-nov.pdf
%L hal-01235349
%U https://hal.science/hal-01235349
%~ CNRS
%~ UNIV-AMU
%~ EC-MARSEILLE
%~ INSMI
%~ I2M
%~ I2M-2014-
%~ ANR