LINEAR NESTED ARTIN APPROXIMATION THEOREM FOR ALGEBRAIC POWER SERIES

Francisco-Jesus Castro-Jiménez (1) , Guillaume Rond (2)

1 DALG-US - Departamento de Algebra [Sevilla]
2 I2M - Institut de Mathématiques de Marseille

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.

Domaines: Algèbre commutative [math.AC]; Géométrie algébrique [math.AG]

Francisco-Jesus Castro-Jiménez, Guillaume Rond. LINEAR NESTED ARTIN APPROXIMATION THEOREM FOR ALGEBRAIC POWER SERIES. 2015. ⟨hal-01235349v2⟩