REMARKS ON ARTIN APPROXIMATION WITH CONSTRAINTS

Dorin Popescu (1) , Guillaume Rond (2)

1 IMAR - "Simion Stoilow" Institute of Mathematics
2 I2M - Institut de Mathématiques de Marseille

We study various approximation results of solutions of equations f (x, Y) = 0 where f (x, Y) ∈ K[[x]][Y ] r and x and Y are two sets of variables, and where some components of the solutions y(x) ∈ K[[x]] m do not depend on all the variables x j. These problems were highlighted by M. Artin.

Domaines: Algèbre commutative [math.AC]

Dorin Popescu, Guillaume Rond. REMARKS ON ARTIN APPROXIMATION WITH CONSTRAINTS. Osaka Journal of Mathematics, 2019, 56 (3), pp.431-440. ⟨hal-03455277⟩