LINEAR NESTED ARTIN APPROXIMATION THEOREM FOR ALGEBRAIC POWER SERIES Auteur(s): Castro-Jiménez Francisco-Jesus, Rond G.
Ref HAL: hal-01235349_v2 Ref Arxiv: 1511.09275 Ref. & Cit.: NASA ADS Exporter : BibTex | endNote Résumé: 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. |