LINEAR NESTED ARTIN APPROXIMATION THEOREM FOR ALGEBRAIC POWER SERIES

Abstract : 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.
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https://hal.archives-ouvertes.fr/hal-01235349
Contributor : Guillaume Rond <>
Submitted on : Monday, November 30, 2015 - 9:48:09 AM
Last modification on : Monday, March 4, 2019 - 2:04:18 PM
Long-term archiving on : Tuesday, March 1, 2016 - 11:11:49 AM

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  • HAL Id : hal-01235349, version 1
  • ARXIV : 1511.09275

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Francisco-Jesus Castro-Jiménez, Guillaume Rond. LINEAR NESTED ARTIN APPROXIMATION THEOREM FOR ALGEBRAIC POWER SERIES. 2015. ⟨hal-01235349v1⟩

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