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About: Artin approximation theorem     Goto   Sponge   NotDistinct   Permalink

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In mathematics, the Artin approximation theorem is a fundamental result of Michael Artin in deformation theory which implies that formal power series with coefficients in a field k are well-approximated by the algebraic functions on k. More precisely, Artin proved two such theorems: one, in 1968, on approximation of complex analytic solutions by formal solutions (in the case ); and an algebraic version of this theorem in 1969.