|LINEAR NESTED ARTIN APPROXIMATION THEOREM FOR ALGEBRAIC POWER SERIES |
Auteur(s): Castro-Jiménez Francisco-Jesus, Rond G.
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Ref Arxiv: 1511.09275
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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.
Commentaires: We have added a reference to a paper of E. Bierstone and P. Milman in which our Proposition 5.1 is proven.